haber + participle — the perfect tenses for completed and hypothetical past actions.

• heyo — auxiliary haber, present; pairs with participle for present perfectI have (done)
• hastú — auxiliary haber, presentyou have (done)
• haél/ella/usted — auxiliary haber, presenthe/she/you (formal) has/have (done)
• hemosnosotros — auxiliary haber, presentwe have (done)
• hanellos/ellas/ustedes — auxiliary haber, presentthey/you (plural) have (done)
• habladoparticiple of hablar (-ar verbs → -ado); regularspoken
• comidoparticiple of comer (-er verbs → -ido); regulareaten
• vividoparticiple of vivir (-ir verbs → -ido); regularlived
• he habladoyo (hablar) — present perfect (pretérito perfecto); haber + participleI have spoken
• has comidotú (comer) — present perfect; participle never changes for gender/numberyou have eaten
• hemos vivido aquínosotros (vivir) — present perfect; recent/relevant pastwe have lived here
• habíayo / él / ella — auxiliary haber, imperfect; pairs with participle for pluperfectI/he/she had (done)
• habíastú — auxiliary haber, imperfectyou had (done)
• habíamosnosotros — auxiliary haber, imperfectwe had (done)
• había comidoyo (comer) — pluperfect (pluscuamperfecto); an action done before another past actionI had eaten
• hechoparticiple of hacer — IRREGULAR (not *hacido)done / made
• dichoparticiple of decir — IRREGULARsaid / told
• vistoparticiple of ver — IRREGULARseen
• puestoparticiple of poner — IRREGULARput / placed
• escritoparticiple of escribir — IRREGULARwritten
• vueltoparticiple of volver — IRREGULARreturned / come back
• abiertoparticiple of abrir — IRREGULARopened
• rotoparticiple of romper — IRREGULARbroken
• no había visto nadayo (ver) — pluperfect with irregular participle vistoI had not seen anything
• habríayo / él / ella — auxiliary haber, conditional; pairs with participle for conditional perfectI/he/she would have (done)
• habría vivido en Españayo (vivir) — conditional perfect (condicional compuesto); a hypothetical past actionI would have lived in Spain
• habríamos hecho másnosotros (hacer) — conditional perfect with irregular participle hechowe would have done more
• hayayo / él / ella — auxiliary haber, present subjunctive; pairs with participle for perfect subjunctive(that) I/he/she has/have (done)
• hayastú — auxiliary haber, present subjunctive(that) you have (done)
• espero que haya llegadoél/ella (llegar) — perfect subjunctive (perfecto de subjuntivo); after esperar queI hope he/she has arrived
• es bueno que hayas dicho la verdadtú (decir) — perfect subjunctive with irregular participle dichoit is good that you have told the truth