As a Buddhist, how shall we make sense of the notion that there is no such thing as a Soul? The three marks of existence is: Impermanence, Suffering, and No-Self.
If there is no-self, then there is no Soul.

Our cognitive abilities is the result of the physical (Brain organ) and the non-physical (five Skandhas)

In meditation, we are taught to observe the changes of our thoughts, which I presume is the result of the five Skandhas as well.

The question is, if there is no-self and no soul, then who is observing my thoughts? Am I wrong to say they are my thoughts? Who am I? And who is answering my question in this forum?
As a Buddhist, how shall we make sense of the notion that there is no such thing as a Soul?
I'm not sure why you think that &quot;Soul&quot; is a helpful belief.
I think that &quot;soul&quot; is usually taught as being/meaning something permanent, which maybe contradicts the doctrine (or observation) that &quot;things&quot; (or &quot;everything&quot;, or &quot;compound things&quot;) are impermanent (anicca).
I think that what we do with (&quot;make sense of&quot;) the notion (of non-self) is maybe avoid &quot;suffering&quot; views like &quot;I can't get what I want&quot; and &quot;I can't keep what I have&quot; and &quot;I am dying&quot; and so on -- and maybe, instead, develop views that are closer to being true (or avoid &quot;attaching&quot; to any such views).
The question is, if there is no-self and no soul, then who is observing my thoughts?
It's conventional (in life and in language) to assume that there's an agent.
For example if you see some writing, you might assume that &quot;someone&quot; wrote it, to ask &quot;who wrote this?&quot; -- conventionally the existence of &quot;the writing&quot; proves (or implies) the existence of &quot;the writer&quot;.
That's a dangerous generalisation though: if you see a creature, can you assume a creator?
Some people use logic like &quot;The universe (also called &quot;creation&quot;) exists, therefore God must have created it&quot; -- but perhaps that's not a very provable, testable, and/or useful statement.
If you look at a rock, for example: did someone create it? Buddhism might say that &quot;there were conditions as a result of which a rock exists&quot; ... maybe many conditions including atoms, gravity , heat, time, wind and water ... but that's not the same thing as saying &quot;there's a creator&quot;.
In the same way, the fact that there's &quot;a thought&quot; doesn't imply that there's &quot;a thinker&quot;.
Am I wrong to say they are my thoughts?
I think this topic -- How is it wrong to believe that a self exists, or that it doesn't? -- suggests that it's unwise to do so.
Problems (suffering) arise with attachment, with craving, with &quot;I&quot;-making (having wrong views about self).
To some extent, I think that views are a matter of choice. For example perhaps I could choose to believe that my battery-power flashlight gives light because there's a demon or a god inside it, but I prefer not to (I think it wouldn't be a helpful belief).
Who am I?
I think the suttas define this question as the result of unwise attention.
For example here:

A thicket of wrong views
&quot;There is the case where an uninstructed, run-of-the-mill person... does not discern what ideas are fit for attention, or what ideas are unfit for attention. This being so, he does not attend to ideas fit for attention, and attends instead to ideas unfit for attention... This is how he attends inappropriately: 'Was I in the past? Was I not in the past? What was I in the past? How was I in the past? Having been what, what was I in the past? Shall I be in the future? Shall I not be in the future? What shall I be in the future? How shall I be in the future? Having been what, what shall I be in the future?' Or else he is inwardly perplexed about the immediate present: 'Am I? Am I not? What am I? How am I? Where has this being come from? Where is it bound?'
&quot;As he attends inappropriately in this way, one of six kinds of view arises in him: The view I have a self arises in him as true &amp; established, or the view I have no self... or the view It is precisely by means of self that I perceive self... or the view It is precisely by means of self that I perceive not-self... or the view It is precisely by means of not-self that I perceive self arises in him as true &amp; established, or else he has a view like this: This very self of mine — the knower that is sensitive here &amp; there to the ripening of good &amp; bad actions — is the self of mine that is constant, everlasting, eternal, not subject to change, and will endure as long as eternity. This is called a thicket of views, a wilderness of views, a contortion of views, a writhing of views, a fetter of views. Bound by a fetter of views, the uninstructed run-of-the-mill person is not freed from birth, aging, &amp; death, from sorrow, lamentation, pain, distress, &amp; despair. He is not freed, I tell you, from suffering &amp; stress.
&quot;The well-instructed disciple of the noble ones... discerns what ideas are fit for attention, and what ideas are unfit for attention. This being so, he does not attend to ideas unfit for attention, and attends [instead] to ideas fit for attention... He attends appropriately, This is stress... This is the origination of stress... This is the cessation of stress... This is the way leading to the cessation of stress. As he attends appropriately in this way, three fetters are abandoned in him: identity-view, doubt, and grasping at precepts &amp; practices.&quot;


This answer, which uses &quot;a rock&quot; and &quot;a flashlight&quot; as an example, might imply a &quot;materialist&quot; view e.g. &quot;people are only physical&quot;; but I didn't mean that, it's defined as unwise to attach such a view (&quot;this is my permanent Self, my eternal Soul&quot;) to anything, including the physical body.
It would also be a mistake to assume the doctrine implies that &quot;nothing matters&quot; -- it's an aspect of the doctrine, not the whole doctrine.