After being taken in by Bruce, Jason received an excellent education and extensive tutoring from both private tutors and Bruce. He has deep knowledge in many subjects including: Science, Math, Medicine, Geography, Criminology, World History and English. As a former Robin, Jason Todd possesses all the skills of someone trained by Batman but lacked the immense experience of Dick and Tim.
After his resurrection, Jason furthered his knowledge in combat by using Talia Al Ghul's fortune to travel the world similar to what his former mentor did, but sought out much deadlier training. Talia also paid for Jason's tutoring in explosives, strategy, tactics, poisons, weapons, vehicles, stealth, antitoxins, assassination and surveillance. Jason has trained his body to peak physical condition, being physically superior to most Olympic athletes but he may be enhanced to perfect and evolutionary human condition due to the healing of the Lazarus Pit.
He has returned to Gotham and proved to be an extremely dangerous martial artist. Jason's fighting style focuses on brutality, strength, and speed; he is shown to have studied over half-a-dozen fighting styles and has proven to be a master of (included but not limited to) Aikido, Capoeira, Karate, Ninjutsu, Savate, Krav Maga, Kickboxing, and Tae Kwon Do; his skill set proven to be enough to fight Batman and Nightwing on equal terms and even stalemating them.
Jason received more advanced training with the ancient martial artist clan, The All-Caste. In all of the history of The All-Caste Jason proved to be the most successful and skilled fighter which he was rewarded by the secrets of The All-Caste in terms of martial arts, fighting meditation and etc to being the only one who have achieved this secrets.
Jason is an extraordinary marksman, even surpassing his ex-mentor thanks to his heavy trainings and natural hand-to-eye talent, being close (maybe even on par) with the likes of Deadshot and Green Arrow. Todd shown to be a master swordsman too, fighting and holding his own against Green Arrow for a long time until he lost. In New52 he did the same thing again with the difference being he gained the upper hand against Oliver, and later on he wields All-Blades with great proficiency against his enemies.
He is also an expert in fields of surveillance, thanks to his early years in Gotham street for waiting and anticipating his targets for his jobs, he's skills improved after his trainings with Batman. Todd is a professional and seasoned pilot too, trained by an ace pilot in middle east to control planes and helicopters ranging from military to civilian types with excellent proficiency. He is also an expert in demolition, trained by a world-known and infamous bombs-expert in Russia, Jason can defuse bombs from advanced military types to improvised ones.
About me: Jason Todd was the second Robin, but was brutally murdered by the Joker. After he was resurrected, Jason learned Batman did nothing to avenge his death. Anguished and seeking vengeance, he initially turned against his mentor and took on the Clown Prince's former identity: the Red Hood. Eventually coming back to the Bat-Family and assembling a team of anti-heroes known as the Outlaws, Jason once again fights for justice...on his own terms. Raised in the slums of the poor side of Gotham City, Jason Todd was a dark haired boy and the son of a petty criminal named Willis Todd. Eventually, Willis was sent to prison and never returned home despite earning his release after a few years. Thus before Willis got sent to prison was the last time Jason ever saw him. This left Jason with Catherine Todd, a drug addicted woman he did not know was not truly his biological mother. In order to survive and for his so-called mother's habit, Jason turned to crime, ripping off car parts for money. Catherine soon died from a drug overdose, and Willis had disappeared after screwing up a job for Two-Face. Jason was left alone on the streets barely surviving, still stealing parts of cars for cash. This led to Batman discovering Jason in an alley stealing the tires off the Batmobile.
Bruce Wayne tried to put Jason in Ma Gunn's school for troubled youths but Jason ran away from the school when he realized it was actually a front for criminal activity. With that option off the table, Bruce took him in as his own and began training him to replace Dick Grayson as Robin. He did not have Dick's cheerful enthusiasm or natural acrobatic skill, but life had made him tough and full of sarcastic wit which made Jason motivated. Secretly, Bruce believed that had he not taken Jason into his home then in a few years time he would be taking Jason in to the police as Batman. So instead, Jason became the new Robin. A memorial case was installed in the Batcave in remembrance of Jason. Over the next decade Jason's death haunted Batman, as much as his parents' death. As this event is considered to be the very few that has made an impact on Bruce's mentality and thoughts about the general concept of Robin
Leading up to the events that would ultimately end in Jason's death, he became more and more reckless in his actions. He began disobeying Batman's direct orders, as well as leaving himself open to being shot on a few occasions. When Batman tells Alfred he is considering making Jason take some time off, Jason interrupts, clearly angry and tells Bruce to talk to Alfred as he storms off. Jason walks towards his old neighborhood and comes across a family friend. While going through some contents he learns that Catherine Todd was not his mother. He also learns that his mother's name started with an "S." He found three names in his Father's address book and looked for them on the Batcomputer. Thinking Batman wouldn't be interested in this sort of investigation, he takes off to go look for his mother. At the same time, the Joker was in the Middle East trying to hijack a nuclear warhead. Jason goes to the first woman, but she was not his mother. Batman, who was looking for both Jason and the Joker in the Middle East, finds Jason and helps him on his quest. The next name is actually world-renowned assassin Lady Shiva. Batman confronts and defeats her in combat and under the effects of truth serum she reveals that she is not Jason's mother either. Finally Jason finds his mother, Sheila Haywood, and all seems well. However the Joker knows Sheila had previously performed "illegal operations on teenage girls" in Gotham. After one resulted in the death of a teen, she was blacklisted as a medical practitioner. Joker uses this to blackmail her. When Batman has to go stop an incident he warns Jason not to go after his mother and the Joker, to wait for back-up. He disobeys Batman's orders once again and goes to confront his mother. He shows her that he is in fact Robin, and she tells him that Joker is long gone, however, he is actually around the corner. Sheila hands her own son over to the Joker, who begins to savagely beat Jason to a pulp with a crowbar . Double-crossing Jason's mother, he leaves them both to die. When Todd awoke, he and his unconscious mother were next to a bomb in a warehouse. His last action was to try to shield his mother from the blast. Batman came in time to see the warehouse explode. He tore through the rubble and found Jason's dead body. Due to the reality warping effects of Superboy-Prime punching his way into the main reality, Jason Todd's corpse was revived in his grave. Still badly injured from what the Joker did to him, he was able to dig his way to the surface and walk over twelve miles before collapsing and being found by a lost couple driving down the road. He was brought to the hospital and treated as a John Doe after slipping into a coma, as he could not provide anyone with answers. He would eventually awaken and escape through the window. However, he had suffered brain damage and remained partially catatonic as he lived on the streets. Instincts and muscle memory were what he survived on. Fighting a homeless man who had attacked him, his moves were witnessed and recognized by a former hired thug he had fought as Robin. The thug called in some old contacts to turn him in for a reward. Word made its way to Talia al Ghul, and she paid to have Jason abducted and brought to her.
Ra's al Ghul was intrigued but unconvinced of his daughter's opinion that Jason was worth anything to them, due to the severe brain damage he had suffered. He decided that Jason would be sent away but remain protected and cared for out of respect for Bruce Wayne. As far as Ra's was concerned, to do anything more with Jason outweighed the potential risk if Batman were to find out. However, Talia disobeyed her father. She took Jason to the Lazarus Pit her father was using and shoved him in. The shock and healing properties of the pit healed Jason's mind. He was confused and panicked, but Talia rushed him away before her father could retaliate. She had little time to explain anything to him, so all she said was for him not to go to Batman and find out the truth instead. He had not been avenged.
Jason did as Talia told him to do and quickly discovered the truth in her words. After his murder, Batman had done nothing more than send the Joker back to jail like his death was just another one of the Joker's crazy schemes. This was too much for Jason to handle so soon. He was only days out of his traumatic revival in the Lazarus Pit, and he was now overwhelmed with grief and rage about what he had learned. In his anguish, he believed Batman only thought of him as an expendable soldier and that his death clearly meant nothing to the dark knight. Riding on the wave of his anger, he headed straight for Gotham City on a mission of revenge.
Jason did not arrive in Gotham City to hunt down the Joker. Instead, his desire for vengeance took him straight to Batman. He used all of his training as Robin to keep surveillance on Batman and orchestrate a setup. He knew all the right places to feed information so that Batman would hear about it, and he fabricated a story about a major gun buy going down in the city. He was waiting when Batman arrived, knowing that Batman would park the Batmobile a certain distance away from the intended destination. He also knew all the Batmobile's security features, allowing him to rig it with an explosive while Batman was gone. This could have been the death of Batman, but when the time came Jason did not pull the trigger. He later explained to Talia that it was because he wanted Batman to know it was him in the end. He wanted to actually face Batman, and he wanted her help to do it.
Who I'd like to meet: Jason emerged in Gotham City as the Red Hood, taking his new identity from the origin of his greatest fear, the Joker. He did not come to fight crime in the city. He came to influence it to avenge his death. He called a meet with the top street dealers in Gotham and informed them that he would be running the drug trade from now on by showing them the severed heads of their top lieutenants he had killed. The new rules were simple. He would get forty percent of the profit, and they would not sell to kids. If they broke that last rule, he would kill them. He also made moves to get the attention of the major crime figure of the time in Gotham, the Black Mask. He disrupted a major weapons shipment coming in from the docks, destroying most of the weapons and activating an Amazo android so Batman and Nightwing would take care of it. What he took from it was a crate of Kryptonite and then acted like he was willing to sell it back to the Black Mask. In return, the Black Mask sent Mr. Freeze to kill him, but he was expecting something of that nature anyway. He took out the hit-men accompanying Mr. Freeze and escaped when Batman and Nightwing showed up, saying all he wanted was the lay of the land.
Done with making his big debut as the Red Hood, he tracked down the whereabouts of the Joker to some abandoned carnival fair ground. He did not kill the Joker, but he did beat the man to near death with a crowbar. Similar to how the Joker originally killed him.
Jason continued his activities as the Red Hood, enforcing his new rules upon the drug trade and warring with the Black Mask's criminal empire. He considered himself a killer and not a murderer. The people he killed were not innocents. Soon, he finally faced off in a battle against Batman that saw them both unmasked before each other, confirming who he really was to Batman.
Now that his identity was no longer a mystery, he broke into Titans Tower to confront Tim Drake, the boy who had replaced him. He he fought with Cyborg and Beast Boy and defeated them easily. Raven was in the tower but Jason decided to allow her to sleep because she was one of the few people that had actually cared for him during his time with the Titans. He wished her to have good dreams for once. He remembered her advices and said she was right when she told him to watch his temper and remembered the he really cared for her safety. He got rid of them so he and Tim would not be interrupted. The two Robins fought with Jason ridiculed the belief that Tim figured out who Batman really was and said that if anything, Batman meant for him to find out. He also ridiculed the idea that even Kolehad a memorial statue in the Tower but not him. He may have only been a Titan for a very brief time, but he had been one. He became impressed with Tim in their fight and started to understands why Bruce chose him as the new Robin and he had to cheat to beat Tim, gassing him and leaving him unconscious to be found by the Titans later. He writes a note in blood on the wall saying "Jason Todd Was Here." Afterward, he observed that Tim was a good Robin. Jason wondered if had he had friends like Tim did when he was Robin, would he have become a better person.
Later, he kidnapped the Joker and ventured to Crime Alley, where they first met and where Bruce Wayne's parents died. He questioned Batman about why he didn't murder Joker to avenge him, and Batman said he refused to kill. They battled and at the same time argued, which Bruce used as a distraction to beat him. Getting the Joker from where he'd hidden him, Jason finally gave him a choice-kill Joker or he would. He counted down from three after tossing Batman a loaded gun, but Batman sliced his neck with a Batarang. Joker detonated explosives then that exploded the platform they were on, ending the fight.
Jason survived the explosion and continued as the Red Hood. While doing routine surveillance on criminals in Gotham, he overheard a conversation Deathstroke was having about having framed Black Lightning for murder. Jason confirmed it and passed the information on to Nightwing. This led to the Outsiders breaking Black Lightning out of Iron Heights.