Place the water in a medium saucepan and bring to a rolling boil.
While the water boils, rinse the rice several times in a fine mesh colander under running water until the water runs clear.
Once the water is boiling, add the rinsed rice to the saucepan, lower the heat to low, cover and simmer the rice (approximately 15 minutes), or until the water is gone and the rice is tender.
Once the rice is cooked turn the rice out onto a baking sheet and spread it out over the baking sheet to cool.
In a small bowl, whisk together the rice vinegar and sugar. Pour the vinegar over the cooling rice. Stir to combine, and continue cooling the rice while preparing the filling.
Prepare a sushi mat by covering with plastic wrap.
Lay a nori sheet, width-wise across the sushi mat.
Wet hands with plenty of water, and place at least ½ cup of the cooled rice onto the nori sheet, spreading it across the entire sheet.
Gently grab two corners of the nori sheet and flip the rice and nori sheet upside down so that now the rice is on the bottom.
Place the sliced avocado and shrimp width-wise across the nori sheet.
Sprinkle with sesame seeds.
Use the mat to tightly roll the sushi, (adjusting the mat as needed) until only the rice is visible after rolling.
Set the roll aside and continue the same process with the remaining ingredients.
Use a sharp knife to carefully slice the rolls into 1" pieces.
Refrigerate until ready to serve.
Serve cold with teriyaki sauce, wasabi, and soy sauce if desired.