A K1 Visa or Fiance Visa) is a type of visa that allows a foreign-citizen fiancé of a U.S. Citizen to enter the United States for the sole purpose of getting married.
The Petition for Alien Relative allows a U.S. citizen or Lawful Permanent Resident to sponsor a qualified relative for a green card) in the United States.
AOS is the process through which a foreign national applies for lawful permanent resident status in the United States. It can be a complicated undertaking.
I-601 Application for Waiver of Grounds of Inadmissibility
A waiver may be needed if an immigrant has been unlawfully present in the U.S., or broken U.S immigration / criminal / civil laws while outside the U.S.
Naturalization grants U.S. citizenship to a foreign national after they fulfill the requirements established by Congress in the Immigration and Nationality Act.