We've just started with this new notation in class and I'm just trying to get a little more insight into the basics so have a few very basic questions if someone here can help? 1) dxμ = (dt,dx,dy,dz) I understand thats it's just a four-vector with four componants but, what would dxμ be equal to? the same thing? 2) FREE INDICES what does this term mean? free to do what? i.e. "AμAμ is a scalar because you have no free indices" Do the upper and lower indices pair? similarly: "gμvgμv is also a scalar as it has no free indices" also "AμBv has two free indices" Why because they are not paired, what does all this mean? Thanks for any points in the right direction.