The true nature of atma as described by Gita and upanishad..

In chapter 2 of Gita lord krishna tells about atman for the first time. But before that he tells
   nasato vidyate bhavo,nabhavo vidyate satah
   ubhayor api drsto ’ntas,tv anayos tattva-darshibhih
                                                         .......B.g.chap2..sloka..16
English translation-"Those who are seers of the truth have concluded that of the nonexistent  there is no endurance and of the eternal  there is no change. This they have concluded by studying the nature of both."
Who is this destructible? Lord krishna says
             antavanta ime deha,nityasyoktah saririnah
          anasino ’prameyasya,tasmad yudhyasva bharata
                                                                        .......B.g.chap2..sloka..18
English translation-"The material body of the indestructible, immeasurable and eternal living entity (soul or atman) is sure to come to an end; therefore, fight, O descendant of Bharata."
So it is clear that soul is undestrucible..it is the only truth, and this living body is untruth.
Describing characterstics of atman lord krishna says..
na jayate mriyate va kadacin,nayam bhutva bhavita va na bhuyah
ajo nityah sasvato ’yam purano,na hanyate hanyamane sarire 
                                                        .......B.g.chap2..sloka..20
English translation-"For the soul there is neither birth nor death at any time. He has not come into being, does not come into being, and will not come into being. He is unborn, eternal, ever-existing and primeval. He is not slain when the body is slain."
 vasamsi jirnani yatha vihaya,navani grhnati naro ’parani
 tatha sarirani vihaya jirnany,anyani samyati navani dehi
                                                 .......B.g.chap2..sloka..22
English Translation:-"As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones."
       nainam chindanti shastrani,nainam dahati pavaka
     na cainam kledayanty apo,na sosayati marutah
                                                .......B.g.chap2..sloka..23

English Translation-"The soul can never be cut to pieces by any weapon, nor burned by fire, nor moistened by water, nor withered by the wind."

  acchedyo ’yam adahyo ’yam,akledyo ’sosya eva ca
  nityah sarva-gatah sthanur,acalo ’yam sanatanah
                                          .......B.g.chap2..sloka..24

English Translation:-"This individual soul is unbreakable and insoluble, and can be neither burned nor dried. He is everlasting, present everywhere, unchangeable, immovable and eternally the same."

avyakto ’yam acintyo ’yam,avikaryo ’yam ucyate
tasmad evam viditvainam,nanusocitum arhasi
                                     .......B.g.chap2..sloka..25

English Translation:-"It is said that the soul is invisible, inconceivable and immutable. Knowing this, you should not grieve for the body."

The fact that atma is indestructible and all powerful is also expressed in Isha Upanishad..



It is motionless, one, faster than mind ; and the Devas (the senses) could not overtake it which ran before.Sitting;, it goes faster than those who run after it. By it, the all-pervading air (Sutratnum) supports the activity of all living beings.
                                         .....isha upanishad..sloka 4

It moves, it is motionless. It is distant, it is near. It is within all, it is without all this.
                                         .....isha upanishad..sloka 5
This concept is explained by lord krishna in Gita where he refers to one who knows and sees atman as tatvadarshi and refers to the rarity of such an individual in chap2 sloka 29.
ascarya-vat pasyati kascid enam,
ascarya-vad vadati tathaiva canyah
ascarya-vac cainam anyah srnoti,
srutvapy enam veda na caiva kascit
                        .......B.g.chap2..sloka..23
English Translation:-"Some look on the soul as amazing, some describe him as amazing, and some hear of him as amazing, while others, even after hearing about him, cannot understand him at all."
The upanishad also goes on to add that.....
Who sees everything in his Atman and his Atman in everything, by that he feels no revulsion.                   .....isha upanishad..sloka 4
This concept is also pointed out by lord krishna..
   vidya-vinaya-sampanne,brahmane gavi hastini
   suni caiva sva-pake ca,panditah sama-darsinah
                             .......B.g.chap5..sloka..18
English Translation:-"The humble sages, by virtue of true knowledge, see with equal vision a learned and gentle brahmana, a cow, an elephant, a dog and a dog-eater [outcaste]."                                          

So, till now we have seen that atman is pure atman is the only truth, atman is indestructible. But lord krishan doesnot stop here in his description of atman and continues his discussion in later chapter over the topic of atman....