What the statute covers
Section 245(a) generally applies to a person inspected and admitted or paroled, and includes an approved VAWA self-petitioner route. The applicant must be eligible for an immigrant visa, admissible and have an immediately available visa when filing. The decision is discretionary. Form I-485 is the application, not an independent grant of eligibility.
Limits and practical context
Section 245(c) contains bars and exceptions. Immediate relatives of U.S. citizens are exempt from certain status and unauthorized-employment bars, but not every ground of inadmissibility or every adjustment restriction. Travel, prior removals and entry history require separate analysis under INA §212 and other provisions.