This article gives a detailed introduction to symmetric spaces of non-compact type and their relation to corresponding semisimple lie groups. This is done more or less from scratch and explicitely without the reader having to know large parts of modern differential geometry
@article{1546, title = {Symmetric Spaces of Noncompact type}, journal = {CUBO, A Mathematical Journal}, volume = {7}, year = {2005}, language = {en}, url = {http://dml.mathdoc.fr/item/1546} }
Moskowitz, Martin. Symmetric Spaces of Noncompact type. CUBO, A Mathematical Journal, Tome 7 (2005) 28 p. http://gdmltest.u-ga.fr/item/1546/