These are comprehensive and well-organized lecture notes for SMA 2371: Partial Differential Equations (PDE) offered to BSc. Biostatistics Year 2 Semester 2 students at JKUAT. The notes are neatly arranged from lecture one to the final topics, making them ideal for class learning, revision, CAT preparation, and final examinations. The notes include detailed explanations, worked examples, step-by-step mathematical derivations, solved exercises, and applications of Partial Differential Equations. Topics covered include: • Review of basic concepts and partial derivatives • Jacobians, surfaces and curves in three dimensions • Simultaneous first-order differential equations • Methods of solving symmetric differential equations • Orthogonal trajectories • Pfaffian differential equations • Linear first-order partial differential equations • Formation of PDEs • Elimination of arbitrary constants and arbitrary functions • Heat, Wave, Laplace and Poisson equations • Separation of variables • Fourier and Laplace Transform methods • Numerous worked examples, tutorial questions and examination-style problems with solutions. These notes are suitable for JKUAT students and other university students studying Mathematics, Statistics, Biostatistics, Engineering, Applied Mathematics or related courses. They are an excellent revision resource for CATs and final examinations.