Yes, we welcome you to use our data on anything that you work on be it for your book, website, research report, presentation, etc. You do not need to request permission from CoinGecko to use any CoinGecko information on any of your publications. Just mention that the data was obtained from CoinGecko and do follow our Branding Guideline.
If you are interested in getting data from CoinGecko, we have a free public API. The documentation for this API is accessible here: https://www.coingecko.com/api
The free public API is subjected to rate limits of 50 requests/minute. The /coins/list endpoint has a rate limit of only 5 requests/minute. Your IP will automatically be banned if you make calls above this rate limit.
If you need higher rate limits, we have a Pro API that is used by multiple crypto companies hosted on a dedicated infrastructure. To enquire about our Pro API, do kindly click on Submit a request at the top of this page. Select 5 - CoinGecko API and do inform us of your interest in subscribing to the CoinGecko Pro API. Our Sales representative will get back to you and share our CoinGecko Pro API deck.