If you have time to see nothing else in Dresden, it should be this and the Frauenkirche. 

One of Europe's richest and probably its oldest public museum (although the Vatican disputes this), the Dresden State Art Collection, inside the Dresden Royal Palace, is also one of its most modern and forward-looking in terms of displaying and interpreting its treasures for visitors. 

Priceless art, opulent court clothing, intricate needlework, even Augustus the Strong's personal garden tools are shown and their significance explained.