I was wondering if anyone has some well organized material that goes through the relationships among the most important stochastic processes like Markov, Ito, Levy, Martingales etc.
Thank you
These online lecture notes and two textbooks listed in this stats.exchange discussion, one of which is free online, are a good introduction to stochastic processes. They also include information on Markov processes, and the lecture notes briefly mentions the Levy property. A shorter introduction to the processes is here.
The above do not detail advanced processes in particular Ito and Martingales. MIT has a great collection of notes on advanced stochastic processes, including Ito and Martingales.
Here are also online PPT notes on the Ito process, a good guide for Martingales, and a good PPT for Levy.