To master the theory of probability and mathematical statistics, practice in solving problems and developing intuition is just as crucial as studying the proofs of theorems. The vast array of problems in this field often makes it challenging for students to transition from lectures to exam questions, and from there to real-world applications. This volume focuses on Markov chains and their applications, a subject that has recently experienced a significant resurgence. Many remarkable theoretical results have emerged in this area, which was long considered a "dead" zone by many specialists. Applied research plays a vital role in the advancement of this field. The topics covered in this book are essential for both contemporary applications—such as financial mathematics, management, telecommunications, signal processing, and bioinformatics—and for classical applications like actuarial mathematics, sociology, and engineering. The authors have compiled a wealth of exercises, each accompanied by comprehensive solutions tailored to the needs and skills of learners. Necessary theoretical insights are provided throughout the text, along with historical digressions that enrich the reader's understanding.