Q:

Book recommendation: Homology and Cohomology

I need to learn some concepts about Homology and Cohomology theory to apply in riemannian geometry basically, but really I have not time to read about that.  
I know just two books of W. S. Massey, Algebraic Topology: An introduction and A basic course of Algebraic Topology,  about this (they're big references here), but I don't know what's the difference between them.  Is there really much difference for a quick reading?  What's the better? 
I would like to know if someone has a quick book or lectures notes about Homology and Cohomology theory to help me. 
Thanks so much. 

A:

Although Amazon says that Massey's Singular Homology Theory is a sequel to Massey's Algebraic Topology: An Introduction, the earlier book is not a logical prerequisite for Singular Homology Theory.  
There are plenty of online lecture notes that might be a right fit for you, for example: http://www.math.harvard.edu/~ctm/home/text/class/harvard/213b/01/html/course/course.pdf.  
Start by googling, pick a set of introductory lecture notes, and try to do the exercises in them.  If you have any questions, ask them here. 