'\' is a special character in C# - it indicates that the following character is a "special code" and should be combined to produce a new character. For example, "\n" is a newline, "\"" is a double quote, and "\\" is a backslash.
static String MyDBConStr = "Data Source=.\\sqlexpress; Initial Catalog=AddressDb; Integrated Security=True";
Or better, prefix teh strign with '@' to turn off backslashes:
static String MyDBConStr = @"Data Source=.\sqlexpress; Initial Catalog=AddressDb; Integrated Security=True";
But you shouldn't do that anyway: connection strings should be stored in a configuration file, so you don't have to recompile your application for each new release or change in the DB server!