To connect a .NET application with SAP system, there are different approaches that you can follow:
Use of SAP PI middleware that offers different protocols and communication framework for integration of two systems. SAP PI/XI enables you to set up cross system communication and integration and allows you to connect SAP and non-SAP systems based on different programming language like Java and SAP ABAP. It provides an open source environment that is necessary in complex system landscape for the integration of systems and for communication.
SAP Process Integration is a middleware to allow seamless integration between SAP and non-SAP application in a company or with systems outside the company.
An application run on different systems that are part of different business units in a company or implemented in a distributed environment between different companies that have a business relationship with each other. In this environment, there is a need for seamless integration and transfer of information between different systems. SAP PI provides a middleware platform that doesn’t deal with how application components are implemented with a business logic and focus more on data exchange between the different components.
You can consider SAP PI as a central instance or middleware that interconnects different systems. This middleware can be referred as SAP PI runtime engine and this communication is called mediated communication. When you compare this communication with a point to point scenario, it is easy to manage the systems and connections. In addition to all this, information related to integration is available at one central point.
Another approach is the use of Internet Communication Framework that can be used to implement REST or SOAP web services. ICF is an inbuilt HTTP framework in SAP system. With ICF, you can develop web applications via web services by writing a so-called handler.
For more details about real Web Services with REST and ICF, you can refer below link: