Here are some basic, intermediate and advanced Next.js projects you can build:

Basic Next.js Projects:

• Blog: A simple blog website is a great starter Next.js project. You'll learn how to use pages, API routes, and Markdown.

• Portfolio: Build a portfolio website to showcase your work. Learn how to organize pages, use CSS modules, and deploy to services like Vercel.

• E-commerce Store: Start with a simple e-commerce store with just static pages for products. Learn the file-based routing in Next.js.

Intermediate Next.js Projects:

• Blog with CMS: Add a CMS like Strapi or Sanity to your blog so you can edit content dynamically. Integrate the API into getServerSideProps.

• E-commerce with Cart: Add a shopping cart, checkout and payment integration to your e-commerce store. Use getServerSideProps and API routes.

• Social Network: Build a social media app where users can post, like, and comment. Learn to integrate with third-party APIs and authentication.

Advanced Next.js Projects:

• E-commerce with Orders: Add order management to your store with order history, tracking, and inventory management.

• Job Board: Build a job listing website with features like search, filtering, application forms, and employer dashboards.

• Course Platform: Create an online course platform where instructors can create and sell courses. Users can enroll, view lessons and make payments.

Those are some example projects at basic, intermediate and advanced levels you can build with Next.js. The complexity increases as you add dynamic content, data fetching, authentication, payments etc.