I've been reading the "Game Physics Engine Development by Ian Millington" book as I've been recommended to (not ended yet) but still quite lost about how to start with the development, don't really know where to begin...
This book is a good introduction, but is outdated. Forget about it.
I recommend all Erin Catto GDC slides, here: https://code.google.com/p/box2d/downloads/list. All slides on this website are pure gold, so do the references.
Take a look into sequential impulses LCP solver.
The most basic dynamics simulation should have rigid bodies and ball-socket joints.
You will also need collision detection, which increases exponentially the time needed to create an physics engine.
Creating a physics engine from scratch without a solid math background such vector calculus is hard. Especifically, to learn about constrained dynamics, which naturally comes from the robotics/mechanics literature. But is not impossible. Is actually a very good experience, IMHO.