The Form I-131 is needed when you wish to leave the United States and return again. It is for a reentry permit, refugee travel document or advance parole travel document, to include parole into the U.S. for humanitarian reasons.
The Form I-129F is used for a number of purposes. It is used to petition to bring your fiancee (K1 Visa) and that person’s children to the U.S. for marriage to you amongst other applications. You search this website for more information.
The Form I-864 is used to show that show that the applying immigrant has enough financial support to live without concern of becoming reliant on U.S. government welfare.
The Form I-485 is needed for an Adjustment of Status after a K1 Visa holder has married in the United States. This is used to apply to adjust your status to that of a permanent resident of the United States.
The Form I-765 allows you to work in the United States. You need to file this application before you start employment in the US. Speak to US Immigration Services about what needs to be filed with this.