I am looking to build a personal project related to Cardano. Are there any documents on libraries or APIs to implement functionalities such as checking balance, transferring funds, etc.?
You can have a look at https://docs.cardano.org/introduction/ for some general information about Cardano.
For APIs and tools, https://developers.cardano.org/tools has a big collection of useful projects that you can use. There is also a getting started section that can be useful: https://developers.cardano.org/docs/get-started/
The cardano-db-sync project follows the chain a inserts on and off chain data into a PostgreSQL database from where it queries using SQL.