These are resources I've found useful in my multivariate stats work:
If you're struggling to understand PCA (Principal Component Analysis) and PLS (Partial Least Squares), this video is a great start. It's by Hervé Abdi; he describes everything visually. The papers on his website have some interesting examples of the techniques (featuring beer, wine, faces...) plus MATLAB code and some worked examples that I've used to verify my own work.
This free software is well documented and is an easy way to calculate sample size and power.
Both are by Glantz, I really like how he writes and the examples are nice and clear:
This one is great for beginners, it covers t-tests, statistical significance: Primer of Biostatistics
This one is more advanced and covers repeated measures ANOVAs etc: Primer of Applied Regression & Analysis of Variance
[The links are to Amazon, but I don't get any affiliate credits, I just think they are terrific books]