I am trying to understand Lambert W function. I am new to this special function. What is the actual meaning of the word two real branches of Lambert W function for any real $x$. How to find the branch point and branch cuts for the Lambert W function. When I used $lambertw(0,1)$ in Matlab i got the real value but for all other branches I got complex values. Actually I couldn't understand that why only these two branches gives real values. Can anyone can explain it clearly?