This book introduces the theory of point processes and random objects. It begins by providing necessary background on inference, probability, measure theory, and stochastic processes. It then covers point process theory, including marked and spatio-temporal point processes. Lastly, the text discusses random objects and shape analysis. Written at the graduate level, this book presents the material in a concise and intuitive way, with many simulations, sample computations, and figures to illustrate the theory.