This book provides a first introduction to the methods of probability theory by using the modern and rigorous techniques of measure theory and functional analysis. It is geared for undergraduate students, mainly in mathematics and physics majors, but also for students from other subject areas such as economy, finance and engineering. It is an invaluable source, either for a parallel use to a related lecture or for its own purpose of learning it.The first part of the book gives a basic introduction to probability theory. It explains the notions of random events and random variables, probability measures, expectation values, distributions, characteristic functions, independence of random variables, as well as different types of convergence and limit theorems. The first part contains two chapters. The first chapter presents combinatorial aspects of probability theory, and the second chapter delves into the actual introduction to probability theory, which contains the modern probability language. The second part is devoted to some more sophisticated methods such as conditional expectations, martingales and Markov chains. These notions will be fairly accessible after reading the first part.Key FeaturesThe book was created out of a given lecture, so it addresses the most common problems of understanding for students and it aims to explain these things more carefullyThe topics are intended to be well-separatedThe sections are covered with minor exercises, such as simple proofs, to train the student’s understandingAppendices for some important notions of measure and integration theory are includedSome constructions, e.g., distributions, densities, some limit theorems or other results, are illustrated by statistical figures

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