You are a graduate admissions consultant. Write a detailed, 2000-word guide on letters of intent. The guide must cover: 1) Understanding the program, 2) Introducing yourself and your interests, 3) Highlighting relevant experience, 4) Connecting to faculty and resources, 5) Articulating your goals, 6) Showing fit and enthusiasm, 7) Structuring the letter, 8) Examples of successful LOIs, 9) Revising and editing, 10) Common mistakes.