using (var repo = new Repository("path/to/your/repo"))
{
    foreach(Branch b in repo.Branches.Where(b => !b.IsRemote))
    {
        Console.WriteLine(string.Format("{0}{1}", b.IsCurrentRepositoryHead ? "*" : " ", b.FriendlyName));
    }
}

using (var repo = new Repository("path/to/your/repo"))
{
    const string commitSha = "5b5b025afb0b4c913b4c338a42934a3863bf3644";
    foreach(Branch b in ListBranchesContainingCommit(repo, commitSha))
    {
        Console.WriteLine(b.Name);
    }
}

private IEnumerable<Branch> ListBranchesContainingCommit(Repository repo, string commitSha)
{
    var localHeads = repo.Refs.Where(r => r.IsLocalBranch);

    var commit = repo.Lookup<Commit>(commitSha);
    var localHeadsContainingTheCommit = repo.Refs.ReachableFrom(localHeads, new[] { commit });

    return localHeadsContainingTheCommit
        .Select(branchRef => repo.Branches[branchRef.CanonicalName]);
}

using (var repo = new Repository("path/to/your/repo"))
{
    repo.CreateBranch("develop");   // Or repo.Branches.Add("develop", "HEAD");
}

using (var repo = new Repository("path/to/your/repo"))
{
    repo.CreateBranch("other", "HEAD~1");   // Or repo.Branches.Add("other", "HEAD~1");
}

using (var repo = new Repository("path/to/your/repo"))
{
    repo.Branches.Remove("BranchToDelete");
}

var description = "branch description"
using (var repo = new Repository("path/to/your/repo"))
{
    var key = string.Format("branch.{0}.description", branch);
    repo.Config.Set(key, description.Replace(Environment.NewLine, string.Empty)); // set description
    repo.Config.Unset(key); // remove description
}