1. The two-fold committed life-styles

loke ‘smin dvi-vidhā niṣṭhā purā proktā mayānagha |

jñāna-yogena sāńkhyānāṃ karma-yogena yoginām || 3-3||

anagha – Oh! Sinless One; asmin – in this; loke – world; dvividhā – two-fold;
niṣṭhā – committed life-styles; purā – in the beginning; mayā – by me;
proktā – was told; jñāna-yogena – in the form of the pursuit of knowledge;
sāńkhyānāṃ – for the renunciate; karmayogena – in the form of the pursuit of action;
yoginām – for those who pursue activity

Oh! Sinless One, the two-fold committed life-style in this world, was told by Me in the beginning û the pursuit of knowledge for the renunciates and the pursuit of action for those who pursue activity.

2. What is to be known is Brahman

jñeyaṃ yattatpravakṣyāmi yajjñātvāmṛtamaśnute |

anādi matparaṃ brahma na sattannāsaducyate || 13-13||

jñeyaṃ yat – what is to be known; tat pravakṣyāmi  – that I will tell clearly;
yat jñātvā – knowing which; amṛtam – deathlessness; aśnute- one gains;
anādimat – that which has no beginning; param – limitless; tat brahma – that Brahman;
na sat – is not-existent; na asat – and not non-existent; ucyate – is said

What is to be known, that I will tell clearly, knowing, which one gains deathlessness, that Brahman, which, it is said, has no beginning, is limitless, neither existent (as an object) nor nonexistent.

3. Brahman exists in the form of all beings

sarvataḥ pāṇipādaṃ tatsarvato ’kṣiśiromukham

sarvataḥ śrutimalloke sarvamāvṛtya tiṣṭhati || 13-13||

tat – that; sarvataḥ pāṇipādaṃ – the one who has hands and feet on all sides;
sarvataḥ akṣi-śrutimalloke – the one who has eyes, heads and mouths (faces) on all sides;
sarvataḥ śrutimat – the one who has ears on all sides; loke – in the people;
sarvam āvṛtya – pervading everything; tiṣṭhati – it remains

That (jñeyam brahma), the one who has hands and feet on all sides, the one who has eyes, heads and mouths (faces) on all sides, the one who has ears on all sides in the (bodies) of the people  remains pervading everything.

4. Īśvara is the essence of all beings (e.g., strength and desire)

balaṃ balavatāṃ cāhaṃ kāmarāgavivarjitam

dharmāviruddho bhūteṣu kāmo ’smi bharatarṣabha || 7-11||

ca – and; bharatarṣabha – O foremost in the clan of Bharata! (Arjuna); balavatāṃ – of the
strong people; kāma-rāga-vivarjitam – that which is free from kāma, desire, and rāga,
attachment; balam – the strength; bhūteṣu – in the beings; dharma-aviruddhaḥ – that
which is not opposed to dharma; kāmaḥ – desire; aham asmi – I am

And in the strong, I am the strength that is free from desire and attachment. In all beings, I am the desire that is not opposed to dharma, O the foremost in the clan of Bharata!

5. Karma-yoga: Manage your likes & dislikes through your free will

indriyasyendriyasyārthe rāgadveṣau vyavasthitau |

tayorna vaśamāgacchettau hyasya paripanthinau || 3-34||

indriyasya-indriyasya-arthe – with reference to the object of every sense organ;
rāgadveṣau – attachment and a version; vyavasthitau – are there; tayoṣ- of these two;
vaśam – spell; na – not; āgacchet – should come under; hi – because; tau – these two;
asya – one’s; paripanthinau – enemies

There is attachment and aversion with reference to every sense object. May one not come under the spell of these two because they are one’s enemies.

6. Karma-yoga: Īśvara is the author of the results of action

karmaṇyevādhikāraste mā phaleṣu kadācana |

mā karmaphalaheturbhūrmā te saṅgo’stvakarmaṇi || 2-47||

karmaṇi – in action; eva – only; te – your; adhikāraþ – choice; phaleṣu – in the results; mā
kadācana – never; karma-phala-hetuḥ – the cause of the results; mā bhūḥ – do not be;
akarmaṇi – in inaction; te – your; saṅgaḥ – attachment; mā astu – let it not be

Your choice is in action only, never in the result thereof. Do not be the author of the results of action. Let your attachment not be to inaction.

7. Karma-yoga: Doing one’s duty is worshipping the lord

yataḥ pravṛttirbhṃtānāṃ yena sarvamidaṃ tatam |

svakarmaṇā tamabhyarcya siddhiṃ vindati mānavaḥ || 18-46||

yataḥ – from whom; bhūtānāṃ pravṛttiḥ – (is) the creation of the beings; yena – by whom;
sarvam idam – all this; tatam – is pervaded; tam – him; svakarmaṇā – through one’s own
duty; abhyarcya – worshipping; mānavaḥ – the human being; siddhim – success; vindati –
gains

Through one’s duty, worshipping him from whom is the creation of the beings, by whom all this is pervaded, a human being gains success.

8. A jñāni understands karma and akarma correctly

karmaṇyakarma yaḥ paśyedakarmaṇi ca karma yaḥ |

sa buddhimānmanuṣyeṣu sa yuktaḥ kṛtsnakarmakṛt || 4-18||

yaḥ – the one who; karmaṇi – in action; akarma – actionlessness; paśyet – would see; ca –
and; yaḥ – the one who; akarmaṇi – in actionlessness; karma – action; (paśyet – would
see); saḥ – that person; manuṣyeṣu – among human beings; buddhimān – wise; saḥ – that
person; yuktaḥ – (is a) yogī; kṛtsna-karmakṛt – who has done everything that is to be done

The one who sees actionlessness in action and action in actionlessness is wise among human beings. That person is a yogī, who has done everything that is to be done.