Background:(you might not be interested so you can skip if you want) I am trying to learn general relativity using the Book Gravitation by Misner, Thorn and Wheeler. The book for the most part seems easy for me to understand but once in a while words i neither heared nor can find the meaning of anywhere are being used. Such a word for example is noncoordinate basis frequently used in exercises in chapter 8. The book is divided in 2 paths for learning 1 for basic things and path 2 for deeper understanding. I am trying path 1 only(lack of time). So now to my questions: If anywhere in the book anything is written about or even defined what a noncoordinate basis: My question is where is it defined or described what it means? If not: What is a noncoordinate basis? Does it have any kind of meaning that distinguishes it from the normal meaning of a basis?(in my own idiot terms a basis of a vector space is a collection of objects from that vector space that when scaled with objects from the field connected to this vector space can reproduce any object of the vector space). If so what distinguishes it?