This thesis is a survey on some field invariants related to quadratic forms. The major part is devoted to the level s=s(F) and the u-invariant u=u(F) of a given field F. The level of a ring  R is defined to be the smallest natural number s such that -1 can be expressed as a sum of s squares in R. If no such number exists s(R) is defined to be infinity. In this thesis, we present that the level of a field must be a power of 2, whereas  for division rings there are examples of levels 2^r and 2^r +1. The u-invariant of a field  F is defined as u(F)=min { n : quadratic forms of dimension >n over F are isotropic }. If no such minimum exists, we define u(F) as infinity. While studying these invariants, another invariant q(F), cardinality of F*/(F*)^2 , is also involved.  The presented results in this survey are due to T.Y. Lam, A. Pfister, J.P. Tignol, D.W. Lewis and W. Scharlau.
 

Keywords: Quadratic forms, quaternion algebras, sums of squares, Pfister forms, level, u-invariant.