ABSTRACT
This chapter provides an illustrated guide to the topics to be discussed with a series of motivating examples. The illustrations involve the recurrence and the transience properties of simple random walks, discussion of some gambling examples, fractals, ancestral evolution processes, as well as some simple examples of Poisson and Bernoulli processes. A young talented fisherman Simeon Denis Poisson was writing a series of essays on fishing techniques in the Loiret river in the spring season 1823. Simeon Denis Poisson was a famous French mathematician and physicist. The mathematician and physicist Martin Kruskal proposes to his students to play one of his new card tricks. Poisson developed his probability theory in 1837 in his work "Research on the Probability of Judgments in Criminal and Civil Matters". The stochastic models were used to count the number of hits of V1 buzz bombs launched by the Nazi army on London, and the outbreaks of war from 1820 to 1950.
