You can override the book.phtml file in Magento 2 using XML.
Book template used to display the address book of the customer with default billing and shipping address at the top of the Address book page.
Magento\Customer\Block\Address\Book
Book Block class contains the native method for the template.
You can override using theme or module level,
1. Theme Level,
app/design/frontend/{Vendor}/{themename}/Magento_Customer/templates/address/book.phtml
2. Module Level,
When you explore the customer_address_index.xml file from the customer module, You can see the address_book block that will be used to display the address book page on the front-end.
In your module create the same XML file, app/code/Module_name/view/frontend/layout/customer_address_index.xml,
<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
<body>
<referenceBlock name="address_book">
<action method="setTemplate">
<argument name="template" xsi:type="string">module-name::address/book.phtml</argument>
</action>
</referenceBlock>
</body>
</page>
Create Template file to override book.phtml,
app/code/Module_name/view/frontend/templates/address/book.phtml
Keep the required content from the Core template and modify your changes. If you want to change an additional section in a page, Override address/grid.phtml in Magento 2.
Clear Cache to see changes,
php bin/magento cache:flush