As I know, the client-side library for SignalR is based on jQuery and this is a bad approach because I don’t need any JavaScript framework in my application but I have to include jQuery to make the SignalR API work.
I want know is there any alternative way/library for connecting to SignalR via JavaScript (without any framework)?
As I read here: https://github.com/SignalR/SignalR/wiki/Faq
SignalR uses different protocols/methods for the best as possible user experience. If the server and the browser support WebSocket it’s going to use this protocol. If you are sure that your clients’ browsers are new enough to support WebSockets than you can skip the JS framework and use directly WebSockets. The client will be with best experience and you won’t need third-parties.
Here you can read how to use the websocket protocol via JavaScript: https://developer.mozilla.org/en-US/docs/WebSockets.