Richard Bowles' Idiot's Guide to Neural Networks

References

Here are some reference books and scientific papers.

An Introduction to Computing with Neural Nets by Richard P. Lippmann, in IEEE ASSP Magazine, April 1987, pages 4 to 22.
All right, it's rather an old article this, but it's relatively easy to read (unlike some I have read) and he keeps the maths down to a minimum. It's the scientific paper that I used to teach myself about neural nets.
Neural Computing, an introduction by R. Beale and T. Jackson (1990), published by the Institute of Physics Publishing, Bristol and Philadelphia.
This is a good book, designed for beginners. Again there is quite a lot of maths, but it is restricted to proving the theories, and can be skipped when you read through it. The book covers neural networks fairly comprehensively.
Connectionism and the Mind by William Bechtel and Adele Abrahamsen (1991), published by Blackwell Publishers (Massachusetts and Oxford). This is a well-known work - lots of people quote it - and yet, it is relatively easy to read. They not only give you the equations in easy-to-digest form, but also explain the background to neural nets and where they fit in on the Artificial Intelligence stage.