LINQ to read XML

Try this.

using System.Xml.Linq;

void Main()
{
    StringBuilder result = new StringBuilder();

    //Load xml
    XDocument xdoc = XDocument.Load("data.xml");

    //Run query
    var lv1s = from lv1 in xdoc.Descendants("level1")
               select new { 
                   Header = lv1.Attribute("name").Value,
                   Children = lv1.Descendants("level2")
               };

    //Loop through results
    foreach (var lv1 in lv1s){
            result.AppendLine(lv1.Header);
            foreach(var lv2 in lv1.Children)
                 result.AppendLine("     " + lv2.Attribute("name").Value);
    }

    Console.WriteLine(result);
}

A couple of plain old foreach loops provides a clean solution:

foreach (XElement level1Element in XElement.Load("data.xml").Elements("level1"))
{
    result.AppendLine(level1Element.Attribute("name").Value);

    foreach (XElement level2Element in level1Element.Elements("level2"))
    {
        result.AppendLine("  " + level2Element.Attribute("name").Value);
    }
}

Or, if you want a more general approach - i.e. for nesting up to "levelN":

void Main()
{
    XElement rootElement = XElement.Load(@"c:\events\test.xml");

    Console.WriteLine(GetOutline(0, rootElement));  
}

private string GetOutline(int indentLevel, XElement element)
{
    StringBuilder result = new StringBuilder();

    if (element.Attribute("name") != null)
    {
        result = result.AppendLine(new string(' ', indentLevel * 2) + element.Attribute("name").Value);
    }

    foreach (XElement childElement in element.Elements())
    {
        result.Append(GetOutline(indentLevel + 1, childElement));
    }

    return result.ToString();
}