A nomenclature (from the IAU and from unofficial sources)

Italics indicate farside features.

Many disallowed or discontinued names from ancient selenographers and from other sources are still useful, and are therefore included in this ABC
(because of some rare digital twist it is (sometimes) impossible to add clickable links into several pages of this ABC. Please take a look in the discussion sections below the lists!)

IAU nomenclature:
Abbe
Abbot
Abel
Abenezra
Abetti
Abul Wáfa
Abulfeda
Abulfeda crater chain (Catena Abulfeda)
Acosta
Adams
Aepinus
Aestatis, Lacus
Aestuum, Sinus
Agarum, Promontorium
Agassiz, Promontorium
Agatharchides
Agatharchides, Rima
Agnes, Mons
Agricola, Montes
Agricola, Rima
Agrippa
Airy
Aitken
Akis
Alan
Al-Bakri
Albategnius
Albert (Luna-17 site)
Al-Biruni
Alden
Alder
Aldrin
Aldrovandi, Dorsa
Alekhin
Alexander
Alfraganus
Alhazen
Aliacensis
Al-Khwarizmi (aka Arabia)
Al-Khwarizmi-King (basin)
Almanon
Al-Marrakushi
Aloha
Alpes, Montes
Alpes, Vallis
Alpetragius (aka Egg-in-a-Nest)
Alphonsus
Alphonsus, Rimae
Alpine Valley (Vallis Alpes)
Alpine Valley Central Rille
Altai, Rupes
Alter
Ameghino
Amici
Ammonius
Amontons
Amoris, Sinus
Ampère, Mons
Amundsen
Amundsen-Ganswindt (basin)
Anaxagoras
Anaximander
Anaximenes
Andel
Anders
Anderson
Andersson
André, Mons
Andronov
Andrusov, Dorsa
Ango
Angström
Anguis, Mare
Ann
Annegrit
Ansgarius
Antoniadi-/ (Basin)
Anuchin
Anville
Apennine Bench Formation
Apennine Front (Apollo-15 site)
Apennine Mountains (Montes Apenninus)
Apianus
Apollo-/ (Basin)
Apollo 11 Site (Statio Tranquillitatis)
Apollo 12 Site (Surveyor crater)
Apollo 14 Site (north of Fra Mauro)
Apollo 15 Site (near Mons Hadley)
Apollo 16 Site (near Descartes and Dollond)
Apollo 17 Site (Taurus-Littrow Valley)
Apollonius
Apollonius, Rimae
Appleton
Appleton-Tsu Basin-/
Arago
Aratus
Aratus CA (LTO: Lorca) ("Krishna" on Rukl's chart 23)
Archerusia, Promontorium.
Archimedes
Archimedes, Montes (aka Montes Lomonosov)
Archimedes, Rimae
Archytas
Archytas, Rima
Ardeshir, Mons
Arduino, Dorsum
Argaeus, Mons
Argand, Dorsa
Argelander
Ariadaeus
Ariadaeus, Rima
Aristarchus
Aristarchus Plateau (aka Wood's Spot)
Aristarchus Rilles (Rimae Aristarchus)
Aristillus
Aristoteles
Arminski
Armstrong
Arnold
Arrhenius
Artamonov
Artamonov, Catena
Artem'ev
Artemis
Artsimovich
Artsimovich, Rima
Aryabhata
Arzachel
Arzachel, Rimae
Asada
Asclepi
Ashbrook
Asperitatis, Sinus
Aston
Atlas
Atlas, Rimae
Atwood
Australe, Mare (Basin)
Autolycus
Autumni, Lacus
Auwers
Auzout
Avery
Avicenna
Avogadro
Azara, Dorsum
Azophi
Unofficial nomenclature:
Abarim, Mons (IAU: crater chain Ball-Pitatus)
Abbe, Vallis (east of Abbe)
Abduh (Lyell A)
Abineri (Strabo A)
Acabe, Mons (IAU: Byrgius and bright nimbus)
Aconitus collis (IAU: Boscovich)
Adlunationis, Sinus (Planitia Descensus, Luna 9 site)
Adriaticum, Mare (IAU: Sinus Medii + SE Sinus Aestuum)
Adriaticus, Portus (Rukl: 41/52)
Aea, Insula (IAU: Cauchy)
Aegyptiacum, Mare (IAU: part of southern Oceanus Procellarum)
Aegyptus (regio) (IAU: southwestern highlands)
Aemus (or Haemus) (IAU: Alexander)
Aerii, Montes (IAU: western end of Montes Carpatus)
Aestuaria Bamelrodia (IAU: Palus Somni)
Aestuum Pyroclastics (see Aestuum, Sinus)
Aethusa, Insula (bright spot SW of Lansberg D)
Aetna, Mons (IAU: Copernicus)
Africae pars (IAU: far western highlands)
Agassiz (Apollo-17 site)
Agricola (Apollo-17 site)
Agricola Straits (see Agricola, Montes)
Air bubbles (the western end of Rupes Cauchy)
Airy swirl (see Airy)
Ajax, Mons (IAU: Cavendish)
Alabastrinus, Mons (IAU: Lichtenberg's bright nimbus)
Alani, Montes (northern rim of Mare Crisium)
Alani's bright spot (high-albedo craterlet in Hewelcke's Mts.Alani)
Alaunus, Mons (IAU: Plutarch and Seneca)
Albategni (IAU: Euctemon?)
Alberti, Promontorium S. (Rukl: 24/25)
Rima Albin / Rupes Albin (south of Lansberg)
Alcuinus (Lubbock N)
Aldrin (IAU: Langemak N)
Alfonsi IX Reg. Cast. (IAU: Democritus)
Alfred Worden's chain (chain of craterlets west of Gruithuisen)
Aller (IAU: Atwood)
Alligator chain (Apollo-15 site)
Alopecia, Insula (IAU: Picard)
Alpha Reed, Vallis (see Mare Ingenii and Rima Paracelsus M)
Alser's alien / Shoeprint (in Robinson)
Alta Vista (see Teneriffe, Montes)
Alter (Albategnius G)
Al-Tusi (King Y) (see link below list)
Amadoca, Palus (IAU: Mare Humboldtianum)
Amadoci, Montes (IAU: Messala area)
Amalfi (IAU: Barrow)
Amanus, Mons (IAU: Delambre)
Amara Mons (location unknown)
Amarae, Paludes (IAU: Mare Spumans and Mare Undarum)
Amari, Fontes (IAU: Cruger's dark floor)
Ambenus, Mons (IAU: bright ray Mason-Mare Frigoris)
America (IAU: Korolev)
Amphitheater (part of Vallis Alpes)
Amundsen (IAU: Scott)
Ancient Newton
Ancient Thebit (see Recta, Rupes)
Anders (IAU: Backlund)
Anderson finger (Anderson L)
Andes mountains (see Humboldtianum, Mare)
Andradae (IAU: Mare Crisium Omega)
Andreus Hills (see Herigonius)
Anemusa, Insula (IAU: bright spot north of Lansberg)(?)
Annae, Mons (IAU: Longomontanus and Wilhelm)
Annae D. Aurel. F. (IAU: Caucasus Gamma)
ANNAE Reg. Fran. (IAU: Arzachel)
Annulatum, Mare (IAU: Mare Orientale)
Annulus Concordiae (between Mts.Cordillera and Mts.Rook)
Annulus Neptuni (IAU: Gassendi)
Anselmi Elect. Mogunt. (IAU: Casatus)
Antaristarchus (Tsiolkovsky, the dark antipode of bright Aristarchus)
Anticaspia (IAU: Mare Humorum)
Antilibanus (IAU: Aliacensis and Werner)
Antitaurus (IAU: chain of Almanon to Playfair)
Antoniadi, Rimae (on the N part of Antoniadi's floor)
Antoniadi (Hecataeus B)
Antural (see Riphaeus, Montes)
A.Pavlov (unofficial name for crater east of Cyrillus)
Apollinis, Promontorium (IAU: Promontorium Laplace?)
Apollinis, Sinus (IAU: Sinus Iridum)
Apollo, Rimae (at the northern part of basin Apollo)
Apollonia, Insula (IAU: Plinius)
Apollonia Minor, Insula (IAU: Ross)
Apollonius, Fossa
Apollo Ridge (A-10 / A-11 region)
Apollo Rille (A-10 / A-11 region)
Appalaches, Rupes (discontinued name, see Al-Khwarizmi)
Arabia (regio) (IAU: SSW limb area)
Arabia (IAU: Al-Khwarizmi)
Arabiae, Paludes (IAU: dark area De Gasparis - Palmieri)
Arago Domes (Arago Alpha and Beta)
Arago 5 (small field of Irregular Mare Patches SE of Maclear / SW of Ross H)
Arati (IAU: Plato Tau)
Arbeit (Apollo-15 site)
Archerusia, Palus (IAU: Julius Caesar)
Archidaeum, Promontorium (see Berzelius and Geminus)
Archimedes, Fossa (Caes's Catena Beer)
Archimedis (IAU: Teneriffe Iota)
Arcuate fractures (south of Arago)
Areesa, Palus (IAU: dark area SW of Fracastorius)
Arenbergii (IAU: Murchison and Pallas)
Argaeus's elongated depression (WSW of Mons Argaeus)
Argentarius, Mons (IAU: Archimedes)
Argolii, Promontorium (IAU: ESE Santbech)
Arietis, Promontorium (IAU: near Vitruvius)
Ariosto (Hirayama C)
Aristarchi (IAU: Archytas)
Aristarchus, Collis
Aristarchus North (small field of Irregular Mare Patches NNE of Aristarchus)
Aristillus's ghost (ghost-crater immediately north of Aristillus)
Aristoteles, Catena (once known as Rima Aristoteles)
Armeniae, Montes (IAU: Gemma Frisius and Goodacre)
Armenter (-898/ +426)
Arms (Apollo-17 site)
Armstrong (IAU: Langemak)
Arondelii (IAU: Lexell A)
Arrhentias, Insula (IAU: bright area north of Moltke)
Arrowhead, The (Mons Hansteen)
Arrowhead (Apollo-15 site)
Artamonov's unnamed companion (the unnamed crater north of Artamonov)
Artemis/Felix/Verne cluster (irregular cluster of craterlets in Mare Imbrium)
Arthur (Anaximander C)
Artsimovich's arrowhead (ENE of Artsimovich)
Arzahel, Promontorium (Rukl: 48)
Arzet (IAU: Zach?)
Asada, Rima (south of Asada)
Asiae pars (IAU: probably SSE limb area)
Asia Minor (regio) (IAU: central highlands)
Astronautorum, Sinus (south of Komarov)
Astronomicum, Mare (IAU: Mare Frigoris)
Ataturk (Romer A)
Atheniensis, Sinus (IAU: Sinus Asperitatis)
Athinagoras (Geminus A)
Athlanticus, Sinus (IAU: Eratosthenes, Timocharis)
Athos, Mons (IAU: Euclides bright nimbus)
Atlas's companion / Atlas bright spot (high-albedo spot E. of Atlas)
Atlas Major (IAU: Bouguer and La Condamine)
Atlas Minor (IAU: Sharp and Sharp B) (Wilkins's Aymat)
Auberi (IAU: Nicolai)
Audus, Mons (IAU: Reiner Gamma, with Reiner?)
Augustini, Flumen S. (IAU: Zupus region)
Aureus, Mons (IAU: Egede A bright nimbus)
Austen (Hirayama M)
Austriaci, Montes (IAU: Montes Apenninus)
Austriacum, Mare (IAU: Mare Imbrium)
Auwers Tholus (dome south of Auwers)
Avani's ghost / Avani Soares's ghost (near Wollaston D)
Avis, Mare (location unknown)
Aymat (Sharp B)
Aytona (= Nachara) (IAU: Montes Harbinger Beta)