The monster, in Mary Shelley's Frankenstein, had many different intentions over the course of the novel.
The monster's most apparent intent was one to connect with another person. In the beginning, the monster wanted to connect with mankind in general. After his first few encounters with mankind (being ran from and attacked), the monster came to realize that man would not accept him easily.
Upon finding the De Laceys, the monster came to know what love of a family was and the devotion people who love each other have for one another. Given that the old man was blind, the monster believed that he could win him over (since the old man would not be able to see his monstrous appearance). After the meeting ended with Felix chasing him from the house, and the De Laceys moving away, the monster came to desire a need for his own family.
Victor's journals caused the monster more pain and isolation. The monster came to find out that Victor had abandoned him. His readings of Paradise Lost showed the monster that he was much more like Satan than the Adam he wished to be.
Knowing that he was alienated by his "father," and desiring the love seen between Felix and Safie, the monster's intent was then to find a mate. Knowing that Victor was the only one who could give him a mate, the monster set out to find Victor.
Therefore, over the course of the novel, the monster's main intent was to find a person who would love and accept him without question. Although this intent took on many faces, the intent was singular. Essentially in the end, the monster' only intent was to be loved by another.