These two are probably the best introductory courses out there right now:
Machine Learning de Andrew Ng, Stanford
Best introductory machine learning course? Maybe a bit dated. (lots of github repos with solutions)
Convolutional Neural Networks de Karpathy, Stanford
Best introductory machine learning course? It says convolutional but the first half deals with machine learning. Really updated!. (lots of github repos with solutions) link to stanford version of the course
Learning from Data, by Abu-Mostafa, 2012 Really short and to the point, a great intro to machine learning from the statistical learning theory perspective (specially good for svm), introducing basic concepts such as overfitting, testing/validation sets, cross validation, model selection, supervised vs non supervised, etc.
Information theory, inference and Learning, by McKay, 2003 Great book for self study, information theory chapters can be skipped, it is a bit general but great for understanding probabilitic and bayesian models, although requires a bit of math saaviness.
Neural Networks and Deep Learning, by Nielsen, 2015, (free online).
Best introduction by far to Neural Networks (feedforward + convolutional). Easy, free and short.
Probabilistic Programming & Bayesian Methods for Hackers, various authors, 2015/2016, (free online, open source) Bayesian and probabilitic models for programmers (easy math!).
Deep Learning Book, by Bengio, 2016, (free online) This is not really "introductory" in the sense of being easy to follow or having few prerequisites, but it is a great intro if you want to work on improving current neural network models.
These books are soft of traditional, and aren't designed for self study, I'd advise you to use them as a reference. They are sorted from easy to difficult. Even though all books cover similar topics, they have different approaches:
Machine Learning/Learning From data: a bit more agnostic, more "pure learning" algorithms
Machine Learning, by Tom Mitchell This is sort of THE classical textbook reference for machine learning stuff. I've read mixed opinions about self-study.
Pattern Recognition, by Theodoridis, 2008 Similar to Bishop's
Pattern Recognition and Machine Learning, by Bishop A sequel to Duda's book, a bit more updated and of similar difficulty.
Pattern Classification, by Duda and Hart, 2000 The classic pattern classification book. A bit dated right now but great for reference.
Machine Learning: a Probabilistic Perspective, by Keving Murphy, 2014. Reputedly difficult and not for self-study, but updated.
Probabilistic graphical models, by Koller, 2009 Great book but a bit disorganized. Also difficult, not recommended for self-study.
The elements of statistical Learning, by Hastie, 2001 Famous for being terse and difficult, not recommended for self-study.
If you are starting out in machine learning, focusing on neural networks the recommended path to take would be:
General knowledge (this can easily take 6 months or more)
Specific neural networks stuff