Greetings ereni,
It sounds as though you're having issues connecting to the Apple Books app on your Mac, and unable to download books successfully. If so, there are great troubleshooting steps which are listed below that can help with resolving this issue.
"Check the system status page: Check Apple’s System Status page to see if there’s an outage for a service in your country or region.Make sure that your device is connected to the internet: Use any web browser to connect to any website. If nothing loads, use another device on the same network to see if it can connect to any website. If no other devices can access the internet, turn off your Wi-Fi router, then turn it on again to reset it. If you still can’t connect to your Wi-Fi network, contact your internet provider for more help. If only your first device can’t connect to the internet, get help with Wi-Fi on your iPhone, iPad, or iPod touch, Apple Watch, Apple TV, or Mac.Update your software: Update to the latest version of iOS or iPadOS, macOS, tvOS, watchOS, or software for your non-Apple device. Then try to connect again.Check the date and time: Make sure that the date and time on your device are set correctly for your time zone. On your Mac: Open System Preferences, then choose Date & Time. If the date and time are incorrect, update them or turn on the option to set date and time automatically."
These steps can be helpful in resolving many connection issues with Apple services. You can also find these steps in the article linked below.
If you can't connect to the App Store, iTunes Store, or other Apple services
Let us know how that goes!