dnd 5e – Would a caster’s AoE spell hit the caster?

Shatter‘s area of effect is a 10-foot radius sphere. The description of a sphere’s area of effect (PHB p. 205) explicitly states:

A sphere’s point of origin is included in the sphere’s area of effect.

Similarly a cylinder’s point of origin is included in the cylinder’s area of effect.

By contrast:

a cone’s (or a cube’s, or a line’s) point of origin is not included in the cone’s (cube’s/line’s) area of effect, unless you decide otherwise.

An evocation specialist wizard could have sculpted the evocation spell shatter around her allies, but not, strictly as written, herself. PHB p. 117:

When you cast an evocation spell that affects other creatures you can see, you can choose a number of them … The chosen creatures automatically succeed on their saving throws against the spell, and they take no damage if they would normally take half damage.

On PHB p. 204, there is wording about spells that allow the caster to pick targets.

A typical spell requires you to pick one or more targets to be affected by the spell’s magic.

There is a sub-section on Targeting Yourself but keep in mind that this is all in the context of spells that require you to pick one or more targets, which does not apply to the shatter spell. For spells that require you to pick targets, you can include yourself or not:

If a spell targets a creature of your choice, you can choose yourself, unless the creature must be hostile, or specifically a creature other than you. If you are in the area of effect of a spell you cast, you can target yourself.

Spells that require you to pick targets don’t explicitly describe an Area of Effect shape. Most of the spells like this (see bless for example) give a range, and say that you can choose N creatures within range. This effectively make the AoE a sphere of radius (the range of the spell) centered on the caster, while making it clear that the Targets rules are in effect (where a caster can target herself or not) rather than the Area of Effect rules (where the caster is targeted if she is within the AoE)