Does evolution only give rise to traits that confer fitness?
I'll try to beat @Remi.b to the suggestion that you review Understanding Evolution as a general overview of evolutionary topics.

For a quick answer: no. 

Sometimes people confuse the great importance of natural selection in evolution with an equivalency between natural selection and evolution. However, there are many many contributors to evolution, many of which do not involve fitness.

I'll list just a couple examples:

Genetic drift is random change in allele frequency because of random sampling of reproductive organisms.

Founder effect is a somewhat related concept, referring to the change in allele frequency in a population that becomes isolated from the rest of the individuals of a species: that population has a selection of traits that might differ from the species as a whole, and lead to future speciation.

There are many more.