Admin Post Update Redirection to Posts Screen

Use the redirect_post_location filter and admin_url() function.

add_filter( 'redirect_post_location', 'wpse_124132_redirect_post_location' );
/**
 * Redirect to the edit.php on post save or publish.
 */
function wpse_124132_redirect_post_location( $location ) {

    if ( isset( $_POST['save'] ) || isset( $_POST['publish'] ) )
        return admin_url( "edit.php" );

    return $location;
}

To redirect to a different url, add everything after the /wp-admin/ portion of the url. I used "edit.php" because the intended url was: http://example.com/wordpress/wp-admin/edit.php.

The redirect_post_location filter is not documented in the Codex Filter Reference. You can find it in the \wp-admin\post.php file near line 73. This is the WordPress code in the trunk version of WordPress:

wp_redirect( apply_filters( 'redirect_post_location', $location, $post_id ) );

As you can see, you can also test the $post_id redirect based on the $post_id or any information obtained from it. To use this second parameter of the filter, you need to pass the priority and _accepted_args_ parameters in the filter call:

add_filter( 'redirect_post_location', 'wpse_124132_redirect_post_location', 10, 2 );

And update the function parameters:

/**
 * Redirect to the edit.php on post save or publish.
 */
function wpse_124132_redirect_post_location( $location, $post_id ) {

    if ( isset( $_POST['save'] ) || isset( $_POST['publish'] ) ) {
        // Maybe test $post_id to find some criteria.
        return admin_url( "edit.php" );
    }

    return $location;
}