Can i create a web part to maintain address book of users

This would be more of a custom module. BUT you might rethink creating your own because Customers already have the ability to have multiple addresses. So if you create a Kentico customer who is related to a Kentico user you can then bring up all their addresses using OOTB controls.

I want to create a form under my accounts page and allow user to add the address, Is than any api to save the address.

Yes, if you check out the Kentico API Documentation you'll find the CustomerInfo and AddressInfo classes along with their respective Providers.

thanks for the class names, I went through them but meana while i found the code which is doing the same job, but the main things is the validation which are applied for this form are not able to configured can you suggest how to configure them <asp:Panel runat="server" ID="pnlAddress"> <asp:Label runat="server" ID="lblError" CssClass="ErrorLabel" Visible="false" EnableViewState="false" /> <cms:UIContextPanel ID="pnlUiContext" runat="server"> <cms:UIForm ID="EditForm" runat="server" ObjectType="Ecommerce.Address" AlternativeFormName="SSDLOrdersAddress_E_commerceSite_Edit" RedirectUrlAfterCreate="/MyAccount/Address" /> </cms:UIContextPanel> </asp:Panel> how can i customize the validations for them.