Tensor Calculus 4a: The Tensor Notation

Tensor Calculus 4b: Position Vector, Covariant Basis, Covariant Metric Tensor, Contravariant Basis

Tensor Calculus 1: The Rules of the Game

Why Tensor Calculus?

Tensor Calculus 22: Riemann Curvature Tensor Geometric Meaning (Holonomy + Geodesic Deviation)

Tensor Calculus 4e: Decomposition by Dot Product in Tensor Notation

Tensor Calculus 3a: The Covariant Basis

Tensor Calculus 23: Riemann Curvature Tensor Components and Symmetries

Tensor Calculus 2: The Two Conflicting Definitions of the Gradient

2. Introduction to tensors.

Coordinate Transformations and Curvilinear Coordinates | Tensor Calculus

Tensor Calculus 20: The Abstract Covariant Derivative (Levi-Civita Connection)

Tensor

Tensor Calculus 14: Gradient explanation + examples

Tensor Calculus 3b: Change of Coordinates

Tensor Calculus 4c: A Few Tensor Notation Exercises

What's a Tensor?

Tensor Calculus 6d: Velocity, Acceleration, Jolt and the New δ/δt-derivative

Tensor Calculus 21: Lie Bracket, Flow, Torsion Tensor (contains error; see pinned comment)

Tensor Calculus Lecture 6c: The Covariant Derivative 2