Thanks to Mind Hacks for pointing out the following tutorial (by Sach Barber) on Artificial Neural Networks (ANNs), and their subsequent implementation in C# (which is similar to C++ in many respects).
From what I've read of it so far, it includes a good overview of the biological inspiration behind ANNs, before moving on to progressively more complex network topologies. One thing I like about this tutorial is that it covers how to actually code these networks - something I find lacking from other sources. The tutorial is split into three parts: the first provides the biology background, and introduces the perceptron; the second part goes through multilayer perceptrons and backpropagation (with C# implementation notes); and the third part explores the use of genetic algorithms for ANN training.
And from the comments provided at the end of the tutorial, it's well worth a read!
Link to the first part of the tutorial.