This thesis explores the theory and application of temporal point processes, with a special focus on Poisson and Hawkes processes. Poisson processes allow for the modeling of independent events that occur at a constant rate of intensity, while Hawkes processes introduce the concept of self-excitement, where each event increases the rate of future events. The first part of the thesis examines the basic concepts and properties of counting processes, introducing homogeneous and non-homogeneous Poisson processes. The intensities of these processes and their applications in various fields are analyzed in detail. The second part of the thesis is dedicated to Hawkes processes. Their structure, conditional intensity function, and branching theory are described. Finally the simulation of Hawkes processes using the thinning algorithm is discussed. The third part of the thesis focuses on one application of Hawkes processes in modeling the spread of information on social networks, with an emphasis on the analysis of retweet cascades, is particularly highlighted. The design of the kernel function, parameter estimation, and popularity prediction are described in detail. The results of this research contribute to a better understanding of the structure and dynamics of events over time and offer significant insights for application in various scientific and practical fields