Check out these first images of Alec in court Monday at the Santa Fe County District Courthouse ... he's in a suit and tie with thick black glasses and has his arms folded over his chest as he sits with his defense team.

Alec seems pretty aware of the camera -- the trial will be live streamed -- and at one point he leans over to one of his attorneys and whispers something in his ear.

Remember ... Alec is charged with involuntary manslaughter in the shooting death of "Rust" cinematographer Halyna Hutchins.

Alec was rehearsing a scene in October 2021 when the gun he was using discharged a live bullet, killing Halyna and wounding director Joel Souza.

The revolver was NOT supposed to have live ammunition and "Rust" armorer Hannah Gutierrez-Reed has already been convicted of manslaughter for her role in the incident, though she is appealing her sentence and claiming the prosecution buried evidence that might have helped her prove the gun fired without Alec pulling the trigger.

Alec has pled not guilty ... but prosecutors claim he was reckless with guns on set leading up to the fatal shooting.