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SErver.Transfer it is used to move to a different aspx page residing on the same server.. Reduces server load by minimizing the roundtrips

server.Execute ... It is used  execute a child ASP page and treat it as part of the parent page. 

Response.Redirect.... it is used to navigate through a different aspx page on the same server or a different server but makes roundtrips to the server therby inc the server load.... Thus use Server.Transfer if you are navigating to the page on the same server as the parent page...

Server.Transfer is used to End the current webform and begin executing a new webform. This method works only when navigating to a Web Forms page (.aspx)
Server.Execute is used to begin executing a new webform while still displaying the current web form. The contents of both forms are combined. This method works only when navigating to a webform page(.aspx)