A Library is a collection of code that we can call from our own code, to help us do things more quickly/easily. For example, Let there is a class for pagination, and we just call the method of that class which does the pagination work.
An API (application programming interface) is a term meaning the functions/methods in a library that we can call to ask it to do things for us – the interface to the library.
An SDK ( (software development kit) is a library (often with extra tool applications, data files and sample code) that aid us in developing code that uses a particular system (e.g. extension code for using features of an operating system (Windows SDK), drawing 3D graphics via a particular system (DirectX SDK), writing add-ins to extend other applications (Office SDK), or writing code to make a device like an Arduino or a mobile phone do what we want)
HAPPY NEW YEAR, 2014