Deciding which math course is the best fit may feel like a real challenge when you arrive to Princeton. Keep in mind that this process often involves a bit of trial and error, and as the first few days of the semester provide additional important information, it will be easy to make adjustments in your schedule if necessary. This process is very flexible and gives excellent results, but the add/drop adjustment step is crucial and the process relies on students to take an active role in gathering information and (re)assessing the situation in the early weeks of the semester. All the general information needed to get started can be found here on these web pages, and various advisors, formal and informal, are available to help with your questions.
The University makes an initial placement recommendation for all incoming students based on the limited information available through standardized test scores. Students refine this initial placement recommendation based on potential majors and other information. Representatives from the math department will be available to answer questions at freshman registration, but this will go more smoothly (and many routine questions can be cleared up ahead of time) if you have done some preliminary research using the placement tools and course information collected here.
Quick Placement Summary: Students with little or no background in calculus are placed in 103, or in 100 if their SAT mathematics scores indicate a need for precalculus review. To qualify for placement in 104 or 175, a student should score 5 on the AB Advanced Placement Examination or a 4 on the BC Advanced Placement Examination. To qualify for placement into 201 or 202, a student should have a score of 5 on the BC Examination. Students who possess in addition a particularly strong interest in mathematics as well as a SAT mathematics score of at least 750 may opt for 203 or 214 or 215 or 216 instead.
For more details consult the general overview of lower division courses, the description of common sequences and the individual course pages in the placement section.