How BLOSUM Matrix is constructed and calculated I would like to ask how BLOSUM matrix is constructed and calculated ? I read the wikipedia and I still do not understand it. I do not understand the mathematical calculations as I have low knowledge about logarithms. 

Maybe could someone give a simple example and then a real-scenario example of how the BLOSUM matrix can be used and calculated, maybe in relation to the Blast algorithm where it uses the BLOSUM scoring matrix to determine high scoring words for each word in the query sequence ?

Also, why are they different types of BLOSUM matrices like BLOSUM62 and so on ?
Sean Eddy wrote an excellent explanation of the BLOSUM Matrix in his Nature Biotechnology paper Where did the BLOSUM62 alignment score matrix come from? He also gives real examples of how one would calculate the score for different amino acid pairs and where the numbers come from.  Further references given at the end of the paper might also be useful reading, specifically: Amino acid substitution matrices from an information theoretic perspective, Methods for assessing the statistical significance of molecular sequence features by using general scoring schemes, and Amino acid substitution matrices from protein blocks.