Tensor mathematics

This lecture focuses on the mathematics of tensors, which represent the core concepts of general relativity. Professor Susskind opens the lecture with a brief review the geometries of flat and curved spaces. He then develops the mathematics of covariant and contravariant vectors, their coordinate transformations, and their relationship to tensors. In the second half of the lecture, Professor Susskind defines tensor operations including addition, multiplication, and contraction, and discusses the properties of the metric tensor.