This book accompanies the reader from the simple, standard Poisson process to its more complex transformations, using a unified framework, showing proofs of basic theorems and references to more difficult results.The reader will also benefit from the empirical applications of the various models to real data in finance and insurance (e.g., stock market crashes and fire accidents), physics and geology (e.g., earthquakes), biology and demography (e.g., births, deaths, and pandemics), ...