Now i will start from the begining. Boots are needed in the begining when ur opponent is wrong from u u cant quickly shunpo to them where boots allow u to catch up to them that allows u to do that. The 3 health pots are used for when u are low from the start and u cant go back cause u dont have enough money or if ur tower is gettin ***ed that when u use it. Now from mejais u dont always get it u can pridict if u will get kills or not from the start so only get this item if u know u are going to do pretty good trough the whole game not for a little while. hextech revolver is a item a kat must have because kat can spam her skills and u while get spell vamp out off each and everyone one of those skills. now the ryalis crystal gives u 80ap and also 500 extra hp which allows u to stay alive and believe it or not 500 hp can determine a lot of things. now why i pick the ionian boots are because of the cd reduction affect. with this and mejais and blue buff while all help u put ur ulti down to 30 sec when u have ulti level 3. But dont get me wrong if u want to u the m boots its ur choice u dont have to use the boots i recommand to u. now the deathcap is most to almost all ap character so i will skip this part. now the void staff while give u bouns ap and also 40% mp not +40 this means if they have 200 mr u while cut trough about 80 of that and if they have only 60 mr u while cut trough about 24 of that mr. The hextech gunblade while give u lots of good things like spell vamp, lifesteal, ap, and also ad which this make this item a very usfull item.