This textbook offers a clear, unified introduction to nonequilibrium statistical mechanics. It combines the classical foundations of equilibrium and nonequilibrium thermodynamics with the field's latest advances. Key topics include Brownian motion, fluctuations theory, the Boltzmann equation, and probability measures in phase space. A common mathematical framework links linear-response theory, transport processes, large-deviation principles, and stochastic dynamics. A companion Volume II will extend the discussion to applications such as anomalous transport, living matter, molecular dynamics, and open quantum systems. The book is written for researchers in applied mathematics, theoretical physics, biophysics, and theoretical chemistry who study nonequilibrium phenomena. It is equally suited to graduate students seeking an accessible path to advanced topics in thermodynamics, transport theory, fluctuation dynamics, and dissipation. It also serves as a reference for graduate courses on  statistical mechanics, stochastic systems, and quantum thermodynamics.