Below are a few entries from different Lexicons (copied from Bibleworks 8)
9159 ἐλπίς, ίδος, ἡ hope; (1) as an expected and awaited good hope, expectation, prospect (AC 27.20); (2) as hopeful confidence in a trustworthy person hope (1TH 2.19); (3) as expectation of a
divinely provided future (the) hope (CO 1.27); (4) as a Christian
attitude of patient waiting, along with πίστις and ἀγάπη
hope (1C 13.13); (5) in combination with prepositions: ἐπ ἐλπίδι in (the) expectation of something (RO 5.2); παῤ ἐλπίδα contrary to (all) expectation (RO 4.18)
25.59 ἐλπίζω ; ἐλπίς, ίδος f: to look forward with confidence to that which is good and beneficial - 'to hope, to hope for, hope.' ἐλπίζω:
ἡμεῖς δὲ ἠλπίζομεν ὅτι αὐτός ἐστιν ὁ μέλλων λυτροῦσθαι τὸν Ἰσραήλ 'and
we had hoped that he would be the one who was going to redeem Israel'
Lk 24.21; ὅτι ἠλπίκαμεν ἐπὶ θεῷ ζῶντι 'because we have placed our hope
in the living God' 1 Tm 4.10. ἐλπίς: περὶ ἐλπίδος καὶ ἀναστάσεως
νεκρῶν ἐγὼ κρίνομαι 'I am on trial (here) because I hope that the dead
will rise to life' Ac 23.6; ἵνα διὰ τῆς ὑπομονῆς καὶ διὰ τῆς
παρακλήσεως τῶν γραφῶν τὴν ἐλπίδα ἔχωμεν 'in order that through
patience and encouragement given by the Scriptures we might have hope'
LSJ Lexicon (Abridged)
14036 ἐλπίς, ίδος, ἡ, (ἔλπω) hope, expectation, Od.;in pl., πολλῶν ῥαγεισῶν ἐλπίδων after the wreck of many hopes, Aesch.;-with
gen. both of subject and object, Πελοποννησίων τὴν ἐλπίδα τοῦ ναυτικοῦ
the hope of the P. in their navy, Thuc.
2. the object of hope, a hope, Ὀρέστης, ἐλπὶς δόμων Aesch.
II. apprehension, fear, Id.
14035 ἐλπίζω, f. Att. ι²ῶ: aor. i ἤλπισα: pf. ἤλπικα:-Pass., aor. i ἠλπίσθην: (ἔλπω):-to hope for, look for, expect, τι Aesch., etc.: c.
inf. fut. or aor. to hope or expect that, Hdt., Att.
2. of evils, to look for, fear, Soph., etc.
3. with inf. pres. it means little more than to think, deem, suppose, believe that, Hdt., Att.
4. c. dat. to hope in. . , τῇ τύχῃ Thuc.; εἴς τινα, ἐπί τινα N.T.
1780 ἐλπίς ἐλπίς (sometimes written ἐλπίς; so WH in Rom. 8:20; Tdf. in Acts 2:26; see (in 2 below, and) the references under the word
ἀφειδον), ἐλπίδος, ἡ (ἔλπω to make to hope), the Septuagint for בֶּטַח
and מִבְטַח, trust; מַחְסֶה that in which one confides or to which he
flees for refuge; תִּקְוָה expectation, hope; in the classics a vox
media, i. e. expectation whether of good or of ill;
1. rarely in a bad sense, expectation of evil, fear; as, ἡ τῶν κακῶν ἐλπίς, Lucian, Tyrannic. c. 3; τοῦ φοβοῦ ἐλπίς, Thucydides 7,
61; κακῇ ἐλπίς, Plato, rep. 1, p. 330 e. (cf. legg. 1, p. 644 c. at
the end); πονηρά ἐλπίς Isa. 28:19, the Septuagint
2. much more frequent in the classics, and always in the N. T., in a good sense: expectation of good, hope; and in the Christian sense,
joyful and confident expectation of eternal salvation: Acts 23:6;
26:7; Rom. 5:4f; 12:12; 15:13; 1 Cor. 13:13; 1 Pet. 1:3; 3:15; ἀγαθή
ἐλπίς (often in secular authors, as Plato, Phaedo 67 c.; plural
ἐλπίδες ἀγαθαί, legg. 1, p. 649 b.; Xenophon, Ages. 1, 27), 2 Thess.
2:16; ἐλπίς βλεπομένη, hope whose object is seen, Rom. 8:24; ὁ Θεός
τῆς ἐλπίδος, God, the author of hope, Rom. 15:13; ἡ πληροθορια τῆς
ἐλπίδος, fullness, i. e. certainty and strength of hope, Heb. 6:11; ἡ
ὁμολογία τῆς ἐλπίδος, the confession of those things which we hope
for, Heb. 10:23; τό καύχημα τῆς ἐλπίδος hope wherein we glory, Heb.
3:6; ἐπεισαγωγή κρείττονος ἐλπίδος, the bringing in of a better hope,
Heb. 7:19; ἐλπίς with the genitive of the subjunctive, Acts 28:20; 2
Cor. 1:7 (6); Phil. 1:20; with the genitive of the object, Acts 27:20;
Rom. 5:2; 1 Cor. 9:10; 1 Thess. 5:8; Titus 3:7; with the genitive of
the thing on which the hope depends, ἡ ἐλπίς τῆς ἐργασίας αὐτῶν, Acts
16:19; τῆς κλήσεως, Eph. 1:18; 4:4; τοῦ εὐαγγελίου, Col. 1:23; with
the genitive of the person in whom hope is reposed, 1 Thess. 1:3 (cf.
Buttmann, 155 (136)). ἐπ᾽ (or ἐφ᾽ -- so Acts 2:26 L T; Rom. 4:18 L;
8:20 (21) T WH; cf. Scrivener, Introduction, etc., p. 565; (but see
above, at the beginning)) ἐλπίδι, relying on hope, having hope, in
hope (Euripides, Herc. fur. 804; Diodorus Siculus 13, 21; ἐπ᾽ ἐλπίδι
ἀγαθή, Xenophon, mem. 2, 1, 187 (Winer's Grammar, 394 (368), cf. 425
(396); Buttmann, 337 (290)): Acts 2:26 (of a return to life); Rom.
4:18; with the genitive of the thing hoped for added: ζωῆς αἰωνίου,
Titus 1:2; τοῦ μετέχειν, 1 Cor. 9:10 (G L T Tr WH); in hope, followed
by ὅτι, Rom. 8:20 (21) (but Tdf. reads διότι); on account of the hope,
for the hope (Buttmann, 165 (144)), with the genitive of the thing on
which the hope rests, Acts 26:6. παρ᾽ ἐλπίδα, beyond, against, hope
(Winer's Grammar, 404 (377)): Rom. 4:18 (i. e. where the laws of
nature left no room for hope). ἔχειν ἐλπίδα (often in Greek writings):
Rom. 15:4; 2 Cor. 3:12; with an infinitive belonging to the person
hoping, 2 Cor. 10:15; ἐλπίδα ἔχειν εἰς (Tdf. πρός) Θεόν, followed by
an accusative with an infinitive Acts 24:15 (εἰς Χριστόν ἔχειν, τάς
ἐλπίδας, Acta Thomae sec. 28; (τήν ἐλπίδα εἰς τόν Ἰησοῦν ἐν τῷ
πνεύματι ἔχοντες, the Epistle of Barnabas 11, 11)); ἐπί with the
dative of person 1 John 3:3; ἐλπίδα μή ἔχοντες (of the heathen) having
no hope (of salvation), Eph. 2:12; 1 Thess. 4:13; ἤ ἐλπίς ἐστιν εἰς
Θεόν, directed unto God, 1 Pet. 1:21. By metonymy, it denotes a. the
author of hope, or he who is its foundation, (often so in Greek
authors, as Aeschylus choëph. 776; Thucydides 3, 57; (cf. Ignatius ad
Eph. 21, 2; ; ad Magn. 11 at the end; ad Philad. 11, 2; ad Trall.
inscr. and 2, 2, etc.)): 1 Tim. 1:1; 1 Thess. 2:19; with the genitive
of object added, τῆς δόξης, Col. 1:27. b. the thing hoped for:
προσδέχεσθαι τήν μακαρίαν ἐλπίδα, Titus 2:13; ἐλπίδα δικαιοσύνης
ἀπεκδέχεσθαι, the thing hoped for, which is righteousness (cf. Meyer
edition Sieffert at the passage), Gal. 5:5 (προσδοκῶν τάς ὑπό Θεοῦ
ἐλπίδας, 2 Macc. 7:14); διά ἐλπίδα τήν ἀποκειμένην ἐν τοῖς οὐρανοῖς,
Col. 1:5; κρατῆσαι τῆς προκειμένης ἐλπίδος, Heb. 6:18 (cf. Bleek at
the passage). -- Zöckler, De vi ac notlone vocis ἐλπίς in N. T.
BGU II. 486:6 (ii/A.D.) ὅτε καὶ οἱ νέοι καρ@ποὶ τὰς βελτίσ]τας παρέχουσιν ἡμεῖν ἐλπίδας. P Oxy VII. 1070:10 (iii/A.D.) a pompous
letter from a man to his wife in which he beseeches Serapis τῶν
χρηστῶν ἐλπίδων τῶν ἐν ἀνθρώποισι νεσνομισμένων (l. νενομð), “for the
good hopes that are held by mankind.” Syll 52985 (i/B.C.) καὶ
ἐφοδεύοντες διεφύλαξαν τ@ὴν πόλιν ἕω]ς τοῦ ἀποκατασταθῆνα@ι] τὸν δῆμον
εἰς βελτίονας ἐλ@π]ίδας. For a disk with the inscr. ἔχω ἐλπίδας καλάς,
see JHS xxxiii, p. 84 ff., BCH xxxviii. (1914), p. 94 ff. Christian
uses of the word are P Oxy VI. 939:9 (iv/A.D.) (= Selections, p. 128)
an affectionate letter regarding a sick mistress—ἐν γὰρ αὐτῇ πάντες
τὰς ἐλπίδας @ἔχομεν, and ib. VII. 1059:1 (v/A.D.) a prayer commencing
Κu,(ριε) θ(ε)έ μου καὶ ὑ ἐρπίς (l. ἡ ἐλπίς) μου. The word is a proper
name in BGU II. 632:20 (ii/A.D.) (= LAE, p. 174) Ἐλπὶς καὶ Φορτου@νᾶτα
(cf. 1 Cor 16:17), and in Syll 865:10 of a slave, see also Cagnat IV.
889:15, 1069:2, 1071:2: cf. Ac 23:6 περὶ ἐλπίδος καὶ ἀναστάσεως νεκρῶν
κρίνομαι, where Lake (Earlier Epp. of St. Paul, p. 16) translates “for
‘Hope’ and a resurrection of the dead am I being judged.” For the
aspirated form ἐφ᾽ ἑλπίδι which WH read in Rom 8:20 cf. Proleg. p. 44,
and see s.v. ἀπελπίζω. In Lat. inscrr. we find Helpis, Helpidius. MGr
ἐλπίδα, ἐρπίδα, ὀρπί(δ)α.
2140 ἐλπίς, ίδος, ἡ hope, expectation, prospect Ac 16:19; 23:6; Ro 4:18; 8:20, 24; 1 Cor 9:10; 2 Cor 1:7. Christian hope Ac 26:6; Ro
5:4f; 1 Cor 13:13; Eph 2:12; 1 Th 1:3; 1 Pt 1:3; (object of) hope 1
Th 2:19; 1 Ti 1:1; hope, something hoped for Ro 8:24; Col 1:5; Tit
2:13; Hb 6:18.