801(e)(2)(A): Admission by a Party Opponent

Rule 801. Definitions That Apply to This Article; Exclusions from Hearsay
(a) Statement. “Statement” means a person’s oral or written verbal expression, or nonverbal conduct that a person intended as a substitute for verbal expression.
(b) Declarant. “Declarant” means the person who made the statement.
(c) Matter Asserted. “Matter asserted” means:
(1) any matter a declarant explicitly asserts; and
(2) any matter implied by a statement, if the probative value of the statement as offered flows from the declarant’s belief about the matter. 
(d) Hearsay. “Hearsay” means a statement that: 
(1) the declarant does not make while testifying at the current trial or hearing; and 
(2) a party offers in evidence to prove the truth of the matter asserted in the statement.
(e) Statements That Are Not Hearsay. A statement that meets the following conditions is not hearsay: 
...
(2) An Opposing Party’s Statement. The statement is offered against an opposing party and: 
(A) was made by the party in an individual or representative capacity... 

To admit an out of court statement as an “admission by a party opponent,” the practitioner needs only to establish that the statement was made by the opponent, and is being offered against them in court.  In a criminal case, the defendant is the party opponent against the state. A party can't offer their own statement against themselves, thus a defendant in a criminal case can’t offer his own self-serving statements.  We'll see later on in this section how that won't prevent them from offering their own statement under authority of a different hearsay rule, but for our purposes here, they can't offer it as a "an admission by a party opponent."

These statements are admissible on the “logic that a party is estopped from challenging the trustworthiness of their own statements...Though our cases have sometimes failed to recognize this aspect of a party’s own statement, we here disavow any precedent indicating that the statement of a party, when being offered against him, is hearsay…And we note that [an admission by a party opponent], unlike statements against interest, need not be against the interests of parties when made; in order to be admissible, the admission need only be offered as evidence against the party.” Trevino v. State, 991 S.W.2d 849, 853 (Tex. Crim. App. 1999).  The proponent must simply prove that the sponsoring witness had firsthand knowledge of the declarant making the statement (proper knowledge) and that the defendant on trial is that declarant.  If it was lawfully obtained (Step 3) and otherwise relevant (Step 4), it will be admitted.