I have some understanding of linear regression and want to understand logit and probit models. What is a good beginners book that helps you develop intuitive understanding of this topic of logistic regression?
I personally like
Both are very readable and specifically designed for beginners. Math is kept at a minimum while emphasis is given on intuition and the methods are illustrated with many examples.
If you are only interested in Logistic regression, then Agresti would be the best choice but if you would also like to see what else is there, besides the classical linear model, Dobson is a good reference.
Hope this helps.
Introduction to statistical learning by James, Witten, Hastie and Tibshirani has a chapter (4) with an introduction of logistic regression. Also provides plenty of alternatives and context as well as code examples in R. You can download it as pdf for free from James' website. http://www-bcf.usc.edu/~gareth/ISL/