I want to manipulate data in excel with some complex functions. It seems that I have to use VBA.
However I don't want to learn it. Is there any other way to do programming in the excel? Some language like C#?
I don't want to create a independent C# application using some interface provided by Excel. Only program in excel, like VBA, but a different language.
Excel has a VBA editor built in to use VBA only. If you want to use another language it would need to be external.
While you could make a C# add in, this is not in the built in editor as you described.
To the best of my knowledge, you simply cannot do this right now. In Office 15 it looks as though you'll be able to use JS:
http://www.zdnet.com/blog/microsoft/microsoft-to-focus-on-html5-and-javascript-for-office-15-extensions/10266
You cannot unfortunately. To program in Excel from within Excel you will have to learn VBA.
To program for Excel, be it VBA, VSTO(C#, VB.Net) you need to understand the Excel Object Model (EOM) without which you cannot do programming for Excel.
You don't need to learn VBA per se if you want to develop Office solutions from C# but as you become familiar with the EOM, you will notice that you automatically develop an understanding for VBA.
EDIT
Excel Object Model from Excel's perspective
Excel Object Model Overview from VS's perspective
You can develop Excel "Add-Ins" in C# using VSTO - Visual Studio Tools for Office (MSDN link).
This is not truly "inside Excel," but once installed your add-in can run without having to start up any external application.