Abstract: It is well known that a normal trace on $B(H)_{+}$ is proportional to the usual trace. On the other hand, it has been an open question whether or not a trace is proportional to the usual one on the set where that trace is finite. In 1966 Dixmier gave negative examples to this problem. Traces $f$ constructed by him have the following properties: $f(a) = 0$ for every operator a of finite rank, but $f(b) = 1$ for some compact operator $b$. Such traces are called Dixmier trace. In this talk I am going to talk about constructing Dixmier traces and deal with some examples.