ArcGIS offers a number of SDKs for GIS application development with the .NET Framework. The links below and in the navigation bar at left direct you to documentation and samples for each SDK.
ArcGIS Explorer
ArcGIS Explorer is a free, downloadable GIS viewer that provides an easy way to explore, visualize, and share GIS information. You, as a .NET developer, can build add-ins that plug in to ArcGIS Explorer. Four types of add-ins are supported: buttons, dock windows, extensions, and galleries. The ArcGIS Explorer SDK provides templates for each of these add-in types.
ArcGIS Mobile
Extend the ArcGIS Mobile field applications with focused tasks and workflows or embed ArcGIS functionality into your existing line-of-business applications using the ArcGIS Mobile SDK. ArcGIS Mobile provides task-centric field applications for vehicle-mounted touch devices and handheld Windows Mobile devices.
ArcGIS Server Web ADF
Build applications with GIS capabilities using the .NET Web Application Developer Framework (.NET Web ADF). The .NET Web ADF is an AJAX-enabled framework for building Web applications built on ASP .Net AJAX. It includes both server-side and client-side controls and libraries. The client-side JavaScript framework is built on MS-AJAX.
ArcObjects
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Build stand-alone applications for ArcGIS Engine or extend ArcGIS Desktop using the ArcObjects SDK. ArcObjects, a library of Component Object Model (COM) components, are the underlying foundation of the ArcGIS platform. These objects can be used to customize ArcGIS or to create your own GIS solution.