An Introduction to Vectors, Vector Operators and Vector Analysis is an essential resource for undergraduate and graduate students in science and engineering. This comprehensive text covers fundamental concepts of vectors and their applications in a single volume. The first unit delves into conceptual and theoretical aspects, exploring the algebraic operations on vectors and the use of Levi-Civita notation. It also delves into curvilinear coordinate systems such as spherical polar and parabolic systems and structures, along with analytical geometry of curves and surfaces. The second unit focuses on the algebra of operators, detailing their types and explaining the equivalence between vector operator algebra and matrix algebra. Eigen vectors and eigen values of linear vector operators are elaborated using vector algebra. The third unit examines vector analysis, covering vector-valued functions of a scalar variable and functions of vector argument (both scalar valued and vector valued), thus addressing both scalar vector fields and vector integration.