The study of the Trinity is of utmost significance. 

Three Reasons to study the Trinity. 

1. It is a fundamental aspect of the Christian faith. 
Heresy and heretic are words that get thrown around pretty lightly these days. These are words that we should be careful to use properly. They quite literally mean that someone has believed something that is false that has excluded them from the faith. One heresy that the Christian faith has always recognized is a rejection of the Trinity. 
The opening words of the Athanasian Creed states, "Whosoever will be saved, before all things it is necessary that he hold the universal* (Christian) faith. Which faith except every one do keep whole and undefiled, without doubt he shall perish everlastingly. And the universal* (Christian) faith is this, that we worship one God in Trinity, and Trinity in Unity; Neither confounding the Persons, nor dividing the Substance."
The very basis of Christian beliefs is the understanding that God exists. We must seek to know Him as He is: One Essense, Three Persons - Three in One. We must not be lazy in our passion to know more about The Eternal King. This is square one, the very basis of everything that we are as Christians. We believe in the Trinity. Do not take this precious doctrine for granted.
2. It is necessary to have a proper understanding of what happened on the cross. 
If we fail to understand the Trinity, then the cross will never make sense. Jesus died on the cross to pay for our sins. To whom was that payment being made? The answer - Jesus was paying our debt to God the Father. If we fail to study the economy (relationship) of the Trinity, then Jesus actions will always remain confusing. Developing a deeper understanding of the Trinity and the relationship between the person of the Godhead will help us to deepen our understanding of the gospel and the atonement that happened on the cross.
3. God Is Love
Christianity teaches that God is eternal. He was never created, He always existed. That is a thought that has kept me awake and perplexed many nights of my life. But, what we must also understand is that God was completely content wihtout us, and had no need to create us. He does not in any way depend on us for satisfaction or fulfilment. God created us simply because He desired to do so. Before creation, He was in an eternal loving relationship between the three persons of the godhead. 
This is foundational to the reality that God is love. If God was not Triune, then he could not have loved until He created something towards which He could show love. For example, the Muslim understanding of allah cannot not contain the notion that the essense of allah is love because love is depends on plurality. They believe that allah existed for eternity past without love. 
What a glorious reality, this truth that God is now, and has always been, showing love. 1 John 4:8 "Anyone who does not love does not know God, because God is love."

It is always worthwhile to learn more about God.
I encourage you, take an hour or two of your next week that would normally go to entertainment (sports, television, scrolling through Facebook statuses, etc.) and spend it studying the Trinity. Below are dozens of links to helpful content that will help you grow in your knowledge of the Triune God. There is something for everyone, beginners and learned theologians alike. 
How well do you know the doctrine of the Trinity? I encourage you to take the Quiz on Tim Challies blog. 
A Quiz on the Trinity.

Here are some great places to start in your journey to learning more about the Trinity.

Good Resources on the Trinity:

(each title is a link to the resource)

The Athanasian Creed

The Athanasian Creed Explained - R.C. Sproul

Free Articles: 

What is the Doctrine of the Trinity? - Matt Perman

Should I Pray to the Father, the Son, or the Spirit? - John Piper

The Trinity Is Not a Contradiction - R.C. Sproul

The Trinity and Culture - Gene Edward Veith 

Divine Architect - Don Kistler

The Biblical Basis of the Doctrine of the Trinity

A Simple Mystery - Burk Parsons

Trinitarian Salvation - R.C. Sproul

Triune Monarchy - R.C. Sproul

Answering Islam: The Historic Case for the Trinity  - K. Dayton Hartman II

Answering Muslim Objections to the Trinity - K. Dayton Hartman II

The Doctrine of the Trinity - Walter Martin

The Trinity in the Old Testament - Peter Wise

A Comprehensive Biblical Defense of the Trinity - Ben Rast

Can You Be a Christian and Deny the Trinity - John MacArthur

Free Audio Clips:

Delighting in the Trinity - Tony Reinke

Theology Refresh: The Doctrine of the Trinity - Jared Wilson

Did the Old Testament Jews Believe In a Triune God? - John Piper

Free Videos:

The Trinity in Two Minutes - John Piper

The Mystery of the Trinity (six part series) - R.C. Sproul

Trinity (9-part video series) - Michael Reeves

A Discussion About the Trinity - James White 

Free Sermons:

The Trinity of Persons - Bruce Ware

The Trinity Defended #1 - James White

The Trinity Defended #2 - James White

Books: 

One God in Three Persons: Unity of Essence, Distinction of Persons, Implications for Life - Edited By Bruce Ware

Father, Son, and Holy Spirit: Relationships, Roles, and Relevance - Bruce Ware

The Forgotten Trinity - James White

The Holy Trinity: In Scripture, History, Theology, and Worship - Robert Letham

What is the Trinity? - R.C. Sproul

Delighting in the Trinity: An Introduction to the Christian Faith - Michael Reeves 

Systematic Theology with good chapters about the Trinity:

Systematic Theology: An Introduction to Christian Belief - John Frame

Systematic Theology: An Introduction to Biblical Doctrine - Wayne Grudem

Christian Theology - Millard J. Erickson

*In the Athanasian Creed, the word catholic has been translated as universal which is its original meaning. This is to avoid confusion with the modern day Roman Catholic religion.