A first course in Probability and Markov Chains presents an introduction to the basic elements in statistics and focuses in two main areas. The first part of the book looks at notions and structures in probability, including Combinatorics, probability measures, probability distributions, conditional probability, inclusion-exclusion formulas, random variables, dispersion indexes, independent random variables as well as Weak and Strong Laws of Large Numbers and Central Limit Theorem. A list of classical probability distributions, both discrete and continuous, is also included. In the second part of the book explores Discrete Time Discrete Markov Chains (DTDMC) which are discussed together with an introduction to Poisson processes and Continuous Time Discrete Markov Chains (CTDMC). The books main focus is in making use of measure theory notations that unify all the presentation, in particular avoiding the separate treatment of continuous and discrete distributions.