Brownian motion is the seemingly random movement of particles suspended in a fluid or the mathematical model used to describe such random movements, often called a particle theory. This book presents topical research in the study of Brownian motion, including Markov chains and Brownian motion models in insect ecology; applications of multifractional Brownian motion to internet traffic; enhanced thermal conductivity of nanofluids using the Brownian motion-based model; Brownian dynamics simulation of surfactant micellar microstructure and rheology and the development of the fractional Brownian motion and its applications on coastal dispersion modelling.