De Vaus, D. (2002) Analyzing Social Science Data: 50 Key Problems and Data Analysis. London: Sage.
Part Seven of this book is about how to carry out multivariate analysis. In particular, look at Problem 41, which reviews what de Vaus calls ‘elaboration analysis’. This looks at what might happen to a relationship between two variables when a third ‘test’ variable is introduced. Problems 46–50 on multiple regression are well worth a read.
Field, A. (2013) Discovering Statistics Using IBM SPSS Statistics, 4th edn. London: Sage.
This covers multiple regression and logistic regression in Chapters 7 and 8 in detail and with explanations of how to use SPSS and interpret the outputs. Similarly with factor analysis (Chapter 17) and log-linear analysis (Chapter 18). There is probably far too much on analysis of variance (Chapters 9–14), which he treats as a form of regression, but Section 10.2.3 explaining why is worth a read.
Hair, J., Black, W., Babin, B. and Anderson, R. (2010) Multivariate Data Analysis: A Global Perspective, 7th edn. Upper Saddle River, NJ: Pearson Education.
This book has been around for over 30 years and is now in its seventh edition. It is regarded by many as the best introduction to multivariate analysis. If you do nothing else, look at Chapter 1, which gives an overview of the whole area including a neat summary of each technique. There is, however, little on SPSS.
Spicer, J. (2005) Making Sense of Multivariate Data Analysis. Thousand Oaks, CA: Sage.
This is a concise, conceptual introduction to multivariate data analysis. There are few symbols and few equations. It covers multiple regression, logistic regression, discriminant analysis, multiple analysis of variance, factor analysis and log-linear analysis. Pay particular attention to the section in each chapter on the trustworthiness of each technique. There is no coverage, however, of SPSS or any other software.