Legato is a name that means something different depending on the instrument you are talking about. Since I am not here to teach you to play piano, I will simply say that legato on the guitar is the use of hammer-ons, pull-offs, and slides, which produces an especially smooth sound. Certain guitarists come to mind when I think of legato, such as Joe Satriani, Allan Holdsworth, Greg Howe, and Shawn Lane. While these guitarists have drastically different styles, what they have in common is very frequent use of legato.
The exercises in this guitar lesson are similar in spirit to my lesson Alternate Picking - Three Note Patterns. In that guitar lesson I had you alternate picking three note patterns that come up in Diatonic Scales. I also had you using various fret hand fingerings to develop your stretching ability to prepare you for more advanced lines. In fact, you could go through that alternate picking guitar lesson and simply use legato to play all the exercises. But I decided to create this separate legato guitar lesson and to add enough variety so that it isn't redundant - for this guitar lesson, we will be in the key of A Major, which is a useful key for you to visualize on the fretboard.
So let's get started with the exercises!