I am familiar with PCA as a linear transformation in order to align the axis of the IV space with the directions of maximal variance in order to possibly be able to reduce the dimensionality of the problem. Are there similar techniques (or can one use PCA itself) when facing a binary classification problem? Like a logistic regression? I.E. Suppose we have a dependent variable we want to predict which only takes values 0 and 1 and we have a lot of features from which to predict, but maybe there are "principal components" in the high dimensional feature space which carry the most explanatory power.
Yes, you can use PCA retaining only certain components as pre-processing step for classification. It is actually pretty common in chemometric classification. However, I prefer PLS as it also uses your class labels and tries to find good separation (which PCA doesn't).
In both cases, keep in mind that this is a data-driven pre-processing and validation of the final model needs data independent also of these pre-processing steps.