How can I get started in developing applications based on cryptocurrency and/or Blockchain?

If you're talking about the bitcoin blockchain, I think the most interesting area right now is metadata, i.e. the ability to attach arbitrary data to bitcoin transactions in something called an OP_RETURN output. This mechanism is used by many applications and protocols such as http://proofofexistence.com (document notarization), http://coinspark.org (assets and messaging), http://factom.org (scalable data storage) to build other applications on top of the bitcoin blockchain. The site http://coinsecrets.org shows the latest metadata being embedded in the blockchain with links to the protocol sites. In terms of books, I recommend Mastering Bitcoin by Andreas Antonopoulos, which provides a great technical overview of the bitcoin protocol and software. Also: here's a great http://startupmanagement.org/2014/12/16/the-ultimate-list-of-bitcoin-and-blockchain-white-papers/ and two of the best blogs in the space: http://gendal.me and http://ofnumbers.com. The mindset is to think of applications which require some kind of trust and control in a centralized third party (notary, registry, exchange), where things could be done much more cheaply and quickly if that centralized third party could be bypassed.