Robot locomotion
Robotics is an interdisciplinarity activity: whether you've practiced some signal processing, machine learning, control theory, numerical optimization, raptor hunting, etc., it helps! The following notes connect dots between the bits of knowledge I find most useful for locomotion in particular. I'd be most happy if they are a good fit for younger roboticists. Shoot me an email if you find anything inaccurate or imprecise (yup, accuracy and precision are not the same thing).
All posts below assume you already know what a controller is. I imagine you've ended up here by searching for a particular topic, yet if you're rather exploring out of curiosity that's great too :) In that case, I'd advise you start from the How do biped robots walk? overview and dig from there into any topic you find interesting.
Kinematics
Dynamics
 Constrained equations of motion
 Equations of motion
 Forward dynamics
 NewtonEuler equations
 Point de nonbasculement
 Principle of virtual work
 Recursive NewtonEuler algorithm
 Screw axes
 Screw theory
 Zerotilting moment point
Contact dynamics
Models
Walking
 Capture point
 Floating base estimation
 How do biped robots walk?
 Linear inverted pendulum model
 Prototyping a walking pattern generator
See also
Physics

Gyroscopic precession
Experiments on angular momentum and torque.

Integration Basics
How to integrate the equations of motion.

The Principle of Least Action
A special lecture by Richard Feynman.
Optimization

An Introduction to Lagrange Multipliers
How Lagrange multipliers arise from optimization constraints.

Conversion from least squares to quadratic programming
How to go from least squares to QP, which is slightly more general.

Quadratic programming in Python
The most common class of convex problems used in optimal control.
OpenRAVE
OpenRAVE is a C++/Python robotics software for forward kinematics and inverse dynamics of robot models. It provides other features not listed here such as symbolic inverse kinematics for serial manipulators. I used it in my PhD and developed the pymanoid library to add wholebody inverse kinematics and model predictive control to it for prototyping humanoid walking controllers.