Hinton and Ng lectures at Coursera , UFLDL , CS224d and CS231n at Stanford, the deep learning course at Udacity , and the summer school at IPAM have excellent tutorials, video lectures and programming exercises that should help you get started.
The online book by Nielsen , notes for CS231n , and blogs by Karpathy , Olah and Britz have clear explanations of MLPs, CNNs and RNNs. The tutorials at UFLDL and deeplearning.net give equations and code. The encyclopaedic book by Goodfellow et al. is a good place to dive into details. I have a draft book in progress.
Theano , Torch , Caffe , ConvNet , TensorFlow , MXNet , CNTK , Veles , CGT , Neon , Chainer , Blocks and Fuel , Keras , Lasagne , Mocha.jl , Deeplearning4j , DeepLearnToolbox , Currennt , Project Oxford , Autograd ( for Torch ), Warp-CTC are some of the many deep learning software libraries and frameworks introduced in the last 10 years. convnet-benchmarks and deepframeworks compare the performance of many existing packages. I am working on developing an alternative, Knet.jl , written in Julia supporting CNNs and RNNs on GPUs and supporting easy development of original architectures. More software can be found at deeplearning.net .
have further information, background and links.