What is the relationship between attribute based encryption (ABE) and access control? So if possible could someone tell me or at least recommend a book.
ABE provides a secure and automatic way to enforce access control, but access control may not involve encryption. 

In the ABE setting, the resources (that one wants to access) are encrypted by a "controller" and then the ciphertexts are made public and each user is granted a key corresponding to its specific access right. Then, the controller doesn't need to interact with the users to manage their access, because such access control enforcement can be guaranteed by the security of the underlying encryption scheme. 

However, in a general access control setting, a "controller" (e.g., an OS or an application) may need to interact with the user (e.g., via an OS access control mechanism or a login system) and grant it the correct access right each time the user wants to access some resources. The resources here may not be encrypted, but are only available to the "controller".