Displaying records from a MySQL database
Dependency injection

Use dependency injection everywhere you can

public class AuthorsController : Controller
{
    private readonly bookisticsEntities _booksEntities;

    public AuthorsController(bookisticsEntities entities)
    {
        _booksEntities = entities;
    }

    public ActionResult Index()
    {
        //all authors on one page can be slow, paging?
        //.ToList() is useless here
       return View(be.authors);
    }

    //default value is not neccessary becouse 0 is an invalid value
    public ActionResult Books(int author_id)
    {
        var author = _booksEntities.authors.SingleOrDefault(a =&gt; a.id == author_id);

        if (author == null)
        {
            return HttpNotFound();
        }

        /*var books = from b in be.books
                    join a in be.authors
                    on b.author_id equals a.id
                    where b.author_id == author_id
                    select b;

        ViewBag.author_name = aut.name;*/

        //pass the author to the view and in the view you can iterate on the author.Books collection
        //if the foreign keys are correct in the database
        //or you setted everything correctly in code first approach
        return View(author);
    }
}


Now the controller expects a bookisticsEntities instance as constructor parameter but the default controller factory in the MVC framework only can use a parameterless constructor so you need a solution for this; use a dependency injection container like Ninject! It's easy to use available through Nuget.

N-tier

It seams to me your application missing one or two (maybe three) application level becouse currently you managing the database directly which is not a best practise. You have to build at leas one level between the MVC and the dataaccess tier which is called business layer (or two: a service layer and under that a business layer). In this way you controller will expect one or more different type of object instances but not your database model!

If you are done whith this you can use simplified models in your application, for example in the Books action method you can use a model which can contain the author's name, identifier and the books also (books can be simplified also). 

Learn Entity Framework

Read a lot about how EF works. :)