Simple logger class in C#
I have two notes to make here,


Extract a public interface from this code, like ILogger&lt;T&gt;, and store (or inject) an ILogger&lt;T&gt; instead of a Logger&lt;T&gt;


This will allow you to create different implementations of your logger type and pass it to the consumers of your logger without them knowing/caring whether it's logging to a console, to a file, or to a typewriter. 

An important use case for that is creating an ILogger implementation for unit tests. You probably don't want your unit tests to have any side effects, so you could create a TestLogger class that implements ILogger and records all the logs to a list instead of a to a file or console.


Handle write access in a safer way


Currently you are not disposing of your StreamWriter instance. Even though you are calling Close you really should be either using a using statement or having a single instance of the stream writer that is accessed through an actor or other thread safe method and is disposed when your logger is disposed.

(Less important, but I would also store the execution path in a static readonly

private static readonly string executionPath = Path.GetDirectoryName(System.Reflection.Assembly.GetExecutingAssembly().Location + "/resources/logging/" + file;

private static void LogToFile(string file, string content)
{
    using (var fileWriter = new StreamWriter(executionPath, true))
    {
        fileWriter.WriteLine(content);
        fileWriter.Close();
    }
}