Here are the Publix deals for the week courtesy of Frugal Coupon Living.
A few highlights:

Egg Beaters – 15 or 16 oz $5/3
USE: $1 June All You Magazine
PRICE:  $.67 each

B1G1 Luigi’s Real Italian Ice – 24 or 36 oz $2.99
USE: $.50 RP 5/2
OR: $.50 RP 5/16
OR: $.50 RP 6/27
 PRICE: $1 each

B1G1 Chi-Chi’s Salsa – 16 oz or Snackers – 4 pk $2.79
USE: $1/2 SS 5/23
PRICE:  $.90 each

B1G1 Musselman’s Apple Sauce – 23 to 24 oz $1.89
USE: $.75 Pubilx Smart Summer Savings Booklet
PRICE: $.20 each

You can see the complete list over here.