Maven and ANT are classified as build tool but Maven has one additional ADVANTAGE that it supports project management, DEPENDENCY management, and standard project layout. Jenkins is a continuous integration tool which is much more superior than a build tool. ANT is the oldest one in a  lot and WIDELY used build tool. A build tool is useful in creating binary ARTIFACTS like JAR file or WAR file. We can easily set up continuous delivery PIPELINE using Jenkins /Hudson which ensures triggering automatic build, test and deploys code base to production. The gang of four ANT,  Maven, Jenkins, and Hudson are tools for building, uni testing, continuous integration and facilitate project management. 

The Jenkins and Hudson are siblings from the same family while one is enterprise offerings and other is open source supported by dev community. Maven offerings are not mere of any other build tool offerings. We need to set up everything in ANT  like souce, build and target directory while Maven has a predefined structure for same. It is said that convention rule dominates Maven while ANT follows configuration rule. The continuous integration tool helps us in triggering build whenever any new changes committed in the source code which ensures if build gets compiled successfully or not. At the same time when compilation is successful, run the unit test and deploy build at a scheduled time ANT vs Maven