A subfield of mathematics called probability theory is concerned with the investigation of randomness and uncertainty. It offers a framework for evaluating and measuring the probability of occurences taking place. In many disciplines, including statistics,economics, engineering,and computer science, it is crucial to comprehend the fundamentals of probability theory. 

Here are some essential ideas and guidelines :

1. Experinment : The experinment is a procedure or action that results in a certain set of results. Examples of experinments include flipping a coin, rolling dice, or conducting a survey.

2. Sample Space : The collection of all potential outcomes makes up the sample soace of an experinment. The sample space for a fair six-sided die would be 1,2,3,4,5 and 6.

3. Event : An event is a subset of the sample space that symbolizes a specific outcome or a group of related outcomes. Events can be either compound (many outcomes) or simple (a single outcome). For instance, rolling an even number on the dice is a complex event, whereas earning a head on a coin flip is a simple event.

4. Probability : Probability is a quantitative indicator of the possibility that an event will occur. A value between 0 and 1, where 0 denotes impossibility and 1 denotes certainty is used express it. P (F) stands for "probability of an event F".

5.  Probability Axioms : The three assumptions that form the foundation of probability theory are as follows :

a) Non-negativity : Any event's probability (P(E)>=0) is a non-negative quantity.

b) Additivity : The likelihood of any group of events coming together (i.e, events that cannot occur concurrently) is equal to the sum of each event's individual probabilities.

c) Normalization : For the entire sample space, there is a chance of 1.

6. Probability of Events : The ratio of favourable outcomes to all potential outcomes in the sample space is used to compute the probability outcomes in the sample space is used to compute the probability of an event E, indicated as P(E).

7. Complimentary Events : The event that comprises of all outcomes not in an event E (designated as E') is said to be its complimentary event. P(E')=1-P(E) gives the probability of the complementary event.

8. Independent and Dependent Events : The difference between independent and dependent events is whether the occurance of one event changes the likelihood of the other. If the occurance of one event changes the likelihood of the other occuring then two events are dependent.

9. Conditional Probability : The probability of an event happening given that another event has already happened is known as conditional probability. The symbol for it is P(E|F), which stands for "the probability of E given F." P(E|F)=P(E F)/ P(F) is the formula for conditional probability, where P(E F) is the probability of both occurances E and F occuring simultaneously.

10. Bayes' Theorem : The Bayes theorem enables  us to revise the likelihood of an event in light of fresh information. The probability of event A given event B is denoted as P(A|B)=(P(B|A)*P(A)/P(B), where P(A|B) is the probability of event A.

Some of the foundational ideas in probability theory include these. You'll comme across ideas like random variables, probability distributions,expected values, and more as you learn more. A strong basis for making wise decisions and comprehending the internet uncertainty in many circumstances is provided by probability theory.