To connect two intersecting or non-intersecting line segments to form a combined path, choose the Pen tool and click on the end point of one segment and then again on the end point of the other segment.

To connect two overlapping points, use the Direct Selection tool (white arrow, keyboard shortcut: A) by clicking and dragging around the points OR The Selection tool (black arrow, keyboard shortcut: V) by holding shift and clicking on each line, or clicking and dragging around the two lines.

Use keyboard shortcut Command-J/Ctrl-J to join them, OR right-click with your mouse and select Join, OR go to the Object menu > Path > Join.

To connect two intersecting lines at the intersection, select both lines with the Selection or Direct Selection tools. Go to the Pathfinder panel and click on Trim, Merge, or Outline (fill/stroke choices may reset). This consequently breaks up the two lines into 4 segments that are grouped together.

To join lines without connecting or combining, select both objects and use keyboard shortcut Command-G/Ctrl-G OR go to Object > Group to group them in the same layer. They can be selected together with the Selection tool or independently within the group using the Direct Selection tool. They can also be ungrouped or regrouped at any time.