Can someone, please, suggest some books for Stochastic Processes with exercises? Can someone, please, recommend me some books about Stochastic Processes,Martingales and Brownian Motion with many exercises? (I would be very happy if some of them are for beginners :D)
Thank you!

Schaum's Outline of Probability, Random Variables, and Random Processes
by Hwei P. Hsu should be the perfect book for you. It really starts out from the beginning and has tons of exercises with solutions for about 90% of them.
And there are a also exercises there that are not so straight forward. 
