Edit Mode buttons for selecting vertices and edges vanished When I am in Edit Mode for my project, the Mesh Select Mode buttons have disappeared!

I loaded the default project and the buttons are where they are supposed to be; the issue is only in my project.
This is because you are in Edit Mode for a Lattice Object. Lattice Objects have one very specific type of Edit Mode and a user can only select vertices.


  A lattice consists of a three-dimensional non-renderable grid of vertices.


Read more on the Manual.