What were the predominant themes of Shakespeare's work?
Are you referring to themes in Hamlet?
If so, revenge is a huge theme in Hamlet. In fact, Hamlet is often called an "Elizabethan revenge play."
Other themes include human mortality or death and fortune or chance. On the level of plot action, Hamlet is an exceedingly mortal work: virtually all of the major characters—Hamlet, Claudius, Gertrude, Polonius, Ophelia, and Laertes—die from unnatural causes by the end of the play; the penultimate scene takes place in a cemetery. Death, decay, and the futility of life fill the spoken thoughts the Danish prince, and the appearance of Ur-Hamlet's tortured ghost leaves us with cold comfort about the afterlife.
A great deal of word play is used in Hamlet; Shakespeare uses a vast number of multivalent terms ranging from gross puns to highly-nuanced words that evoke a host of diverse associations and images. While Hamlet can tell this difference between a "hawk and a handsaw," the play challenges the assumption that language itself can convey human experience or hold stable meaning.
Also, Hamlet contains a great deal of sexual material and innuendo, one in which the charge of "incest" is openly uttered.