Tensor calculus is a prerequisite for many tasks in physics and engineering This book introduces the symbolic and the index notation side by side and offers easy access to techniques in the field by focusing on algorithms in index notation It explains the required algebraic tools and contains numerous exercises with answers making it suitable for self study for students and researchers in areas such as solid mechanics fluid mechanics and electrodynamics ContentsAlgebraic ToolsTensor Analysis in Symbolic Notation and in Cartesian CoordinatesAlgebra of Second Order TensorsTensor Analysis in Curvilinear CoordinatesRepresentation of Tensor FunctionsAppendices Solutions to the Problems Cylindrical Coordinates and Spherical Coordinates All methods are explained in 3 dimensions both in Cartesian in curvilinear coordinates The theory of surfaces of the representation of tensor functions are introduced A variety of problems with detailed solutions engage readers in learning