Quaternions and Clifford Algebra problems

[drake]

Hello, I have some problems with understanding some concepts in Quaternions and Clifford Algebra. For example, where can I learn the basic construcion of Clifford Algebra?
I'm listing the equalities I did not understand and I appreciate it if you can help me with understanding these :

Homework Statement

*What is Cl_p,q ?
*What is R_m^k and why R_m equals to direct sum(or tensor product?) R_m⁰ + R_m¹ + R_m² +...+R_m^m ?
*What is the span of R_m^k ?
*What are those and how can we get the equalities:
R_0,0 = R
R_0,1 = C
R_0,2 = H
R_0,3 = ²H
R_1,0 = ²R

(R stands for Real numbers, C is for Complex numbers and H is for Hamilton)
Thanks :)

 

[drake]

Actually, I still have problems with these, so I was studying some abstract algebra. I found some lecture notes by José Figueroa-O’Farrill which cover the topics. Here they are:
http://empg.maths.ed.ac.uk/Activities/Spin/Lecture1.pdf
http://empg.maths.ed.ac.uk/Activities/Spin/Lecture2.pdf