From agan (much) and hallomai; properly, to jump for joy, i.e. Exult -- be (exceeding) glad, with exceeding joy, rejoice (greatly).
see GREEK hallomai
STRONGS NT 21: ἀγαλλιάωἀγαλλιάω, (ῶ, and (but the active is not used except in Luke 1:47 (ἠγαλλίασα), in Revelation 19:7 (ἀγαλλιῶμεν) L T Tr WH (and in 1 Peter 1:8 WH Tr marginal reading (ἀγαλλιᾶτε), cf. WH's Appendix, p. 169)); 1 aorist ἠγαλλιασάμην, and (with a middle significance) ἠγαλλιάθην (John 5:35; Rec. ἠγαλλιάσθην); a word of Hellenistic coinage (from ἀγάλλομαι to rejoice, glory (yet cf. Buttmann, 51 (45))), often in the Sept. (for גִּיל, עָלַץ, רָנַן, שׂוּשׂ), to exult, rejoice exceedingly: Matthew 5:12; Luke 10:21; Acts 2:26; Acts 16:34; 1 Peter 1:8; 1 Peter 4:13; ἔν τίνι, 1 Peter 1:6, dative of the thing in which the joy originates (cf. Winers Grammar, § 33 a.; B. 185 (160)); but John 5:35 means, 'to rejoice while his light shone' (i. e. in (the midst of) etc.). ἐπί τίνι, Luke 1:47; followed by ἵνα, John 8:56 that he should see, rejoiced because it had been promised him that he should see. This divine promise was fulfilled to him at length in paradise; cf. Winers Grammar, 339 (318); B. 239 (206). On this word see Gelpke in the Studien und Kritiken for 1849, p. 645f.