The download and install button is gray for me and does not work

Hi hasti115,

Thank you for posting in Apple Support Communities. Are you attempting to download and install an iOS update? If so, you'll want to do the following:

1. Confirm you are connected to a strong Wi-Fi network. To connect go to Settings > Wi-Fi. Check out: Connect to Wi-Fi on your iPhone, iPad, or iPod touch - Apple Support.
2. Be sure your iPhone battery is charged to 50% or higher. If not, you'll want to connect to your charger. Check out: Charge the iPhone battery - Apple Support.
3. Confirm you have enough storage to download the update. To confirm your available storage go to Settings > General > iPhone Storage. Check out: How to check the storage on your iPhone, iPad, and iPod touch - Apple Support.

Check out additional steps you can take here: If your iPhone or iPad won't update - Apple Support

Hope that helps!