Java SE - SE stands for Standard Edition. It is the core Java programming platform. It contains all of the libraries and APIs that any aspiring Java programmer should learn.
Java EE - EE stands for Enterprise Edition. It is used when your application demands a very large-scale, distributed system. It is built on top of Java SE, it provides libraries for database access, remote method invocation, messaging, web services, XML processing, and defines standard APIs for Enterprise JavaBeans, servlets, portlets, Java Server Pages, etc.
Java ME - ME stands for Micro Edition. It is used for developing applications for mobile devices and embedded systems like set-top boxes. It provides a subset of the functionality of Java SE, but also introduces libraries specific to mobile devices.
If you are new to Java start with Java SE and move to the others.
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