This chapter is devoted to elements of vector analysis and calculus, which provide the fundamental knowledge and tools needed to deal with the material of the following chapters. We begin with the theory of vector functions of real variables and then introduce the formal nabla operator, \(\nabla \) , together with its properties and applications in various coordinate systems. The chapter continues with vector field theory and its fundamental differential theorems, including the divergence theorem, Stokes’ theorem, Gauss’ theorem, and the continuity equation.