Textbook in PDF format This book provides a comprehensive and in-depth presentation of recent advancements in the Direct Simulation Monte Carlo (DSMC) method, focusing on modern collision algorithms that maintain accuracy even with low particle-per-cell. Drawing from theoretical insights and computational innovations, it bridges fundamental kinetic theory with practical simulation techniques for rarefied gas flows. Structured across ten chapters, the book begins with a discussion of micro- and nanoscale fluid flows, where non-equilibrium effects and rarefaction become dominant. It explores key phenomena in MEMS/NEMS devices, such as velocity slip, temperature jump, Knudsen minimum, and thermal polarization—essential for understanding transport in confined geometries