Transforming shipping rates at the edge with Next.js Advanced Middleware involves using Netlify's Next.js Runtime to deliver geography-based shipping rates to visitors. This requires determining a visitor's location, which can be done using Next.js Advanced Middleware and the Netlify SDK. The middleware function can then use this information to find the correct shipping rate from a JSON file and inject it into the page request. To achieve this, the middleware function must replace the rendered HTML with dynamic data and set the props for the Next.js application. Once deployed to Netlify, the site will be globally available and can be tested with different locations to ensure accurate shipping rates are displayed.