I am a strict monotheist who believes that God is numerically one in person, possesses aseity, being self-existent, self-attesting (serving as His own criterion for truth), and self-justifying. In the Old Testament, God revealed Himself as the LORD (YHVH) and His activities were often referred to as being done by His Spirit, or personified by the His word, His arm, etc. Although God and His Spirit are presented extensively throughout the Old Testament, there is not the slightest hint of any God-Spirit binitarianism taught in the Hebrew Scriptures, which is something we might have expected if God existed ontologically as more than one person. Moving forward to the New Testament, following the incarnation, this same God came to be referred to as the Father, and His Spirit continued to be the selfsame Spirit of the Old Testament who became more commonly called the Holy Spirit (which in the original Greek New Testament is not a proper name, given the variation with which the adjective "holy" modifies the noun "spirit," sometimes coming before it, sometimes after it, sometimes separated from it by several other words, and sometimes not even modifying it at all). However, what distinguishes the New Testament from the Old Testament is the appearance of the Son of God, who we are told is God's word become flesh, or more specifically "God with us" as a true human son. So, what we see is the one true unipersonal God interacting with His creation as the Father (God as God), the Son (God as man), and the Holy Spirit (God in activity) in order to accomplish His purposes, all for His own glory and name's sake. This belief has been historically called Monarchianism, but more recently called Modalism. Monarchianism refers to the "rule of the one" (see Deuteronomy 6:4), whereas Modalism gives the impression that "the one" is hiding behind different masks. Therefore, I don't think these two terms are interchangeable, but for the sake of this article, I will be using them interchangeably because scholars most often refer to Monarchianism as being a type of Modalism.
The vast majority of Christians describe themselves as Trinitarian, but the truth is that many Trinitarians "are practical modalists" (according to Trinitarian scholar Robert Letham on p. xxxii of his book The Holy Trinity). Modalism has a rich history in the church. In fact, the early Christian theologian Tertullian (155 to 220 AD) stated that modalists "always constitute the majority of believers" (Ch. III here), and this statement holds true today (see the video clips of Trinitarian apologist James White below). Tertullian was the first person to use the word "Trinity," but according to Letham, his teachings carried "a bias toward subordination and modalism" (The Holy Trinity, p. 100). In fact, scholars have long recognized that Nicene Trinitarianism gravitates toward modalism (Ibid., p. 290). Again, according to Letham, it was the Modalistic Monarchians who were happiest with the Creed of Nicaea 325 because it defined the Son as being of the same hypostasis as the Father (Ibid., p. 119). The truth is that the Trinity dogma wasn't really established until the Council of Constantinople in 381 AD. For example, the Encyclopedia Britannica says, "It was not until later in the 4th century that the distinctness of the three and their unity were brought together in a single orthodox doctrine of one essence and three persons" (here) and this statement is also verified by the New Catholic Encyclopedia (see p. 193 here).
More recently, Southern Baptist theologian Frank Stagg, speaking on the development of Trinity doctrine, said, "But what began as insistence upon tri-unity eventually became an emphasis upon the threeness and increasing jeopardy to the belief in oneness... To the term trinity were soon added the terms 'persons,' 'three persons,' 'three persons of the Godhead'...Thus trinitarianism was fast on the way to tritheism... This the New Testament never anticipated and does not support" (see p. 7 here). Stagg's concerns were correct because there are many Trinitarian apologists who are teaching that God ontologically has three centers of consciousness, which under any other name would be tritheism. See, for example, social-Trinitarians like William Lane Craig here and the GotQuestions.org website here, and non-social Trinitarians like James White here and Lane Tipton (from 20:20 to 25:03 and again from about 38:00 onward) here. Even Trinitarians, such as Robert Letham and J.V. Fesko, who believe that God ontologically has only one will (i.e., one center of consciousness), paradoxically say that there are three "different" persons in God who are capable of having intra-trinitarian dialogue (see for example, Letham's The Holy Trinity, p. 324 footnote 34, p. 454, and p. 459, and Fesko's The Trinity and the Covenant of Redemption p. 175). And how exactly do non-social Trinitarians like Tipon and Fesko escape the charge of tritheism? Regrettably, not by using Scripture. For Tipton, it is as easy as invoking perichoresis (a concept that was initially developed to explain the incarnation, and only later extended in meaning to describe "interpenetration" between the god persons in 749 AD) and simply asserting that it is not tritheism. For Fesko, again, it's as easy as simply asserting that the intra-trinitarian dialogue doesn't "require" tritheism or social trinitarianism (although he seems to be indirectly admitting that intra-trinitarian dialogue somewhat implies or is characteristic of tritheism and social trinitarianism). This is not to say that there haven't been some Trinitarians who have seen the dangers inherent in the three god persons. For example, Swiss Reformed theologian Karl Barth emphasized that God is unipersonal and exists in "three modes of being" (p. 359 of Church Dogmatics Vol. 1). Although he emphatically denied Modalism, he is often suspected of having been a Modalist, and from what I have read of his opinions on Modalism, it seems to me that he was rejecting a peculiar type of Modalism that posited that the unipersonal God was hiding behind thee masks as an unknown fourth entity. Likewise, Roman Catholic theologian Karl Rahner insisted that there is only one subject in God and famously said, "should the doctrine of the Trinity have to be dropped as false, the major part of religious literature could well remain virtually unchanged" (p. 10-11 of his book Trinity), indicating that the Trinity doctrine held little significance for the bulk of Christian authors. For confirmation that Barth and Rahner held modalistic Trinitarian beliefs, see p. 197 of the New Catholic Encyclopedia here.
It is probably because of difficulties like those mentioned above that some prominent scholars have simply thrown up their hands and chalked everything up to being a mystery. For example, Reformed theologian Louis Berkhof said on page 89 of his Systematic Theology, "The Church confesses the Trinity to be a mystery beyond the comprehension of man. The Trinity is a mystery, not merely in the biblical sense that it is a truth, which was formerly hidden but it now revealed; but in the sense that man cannot comprehend it, and make it intelligible. It is intelligible in some of its relations and modes of manifestation, but unintelligible in its essential nature. The many efforts made to explain the mystery were speculative rather than theological. They invariably resulted in the development of tritheistic or modalistic conceptions of God... The church has never tried to explain the mystery of the Trinity, but only sought to formulate the doctrine of the Trinity in such a manner that the errors which endangered it were warded off." In other words, the Trinity is a mystery both biblically and logically, and if you even attempt to explain it, you'll be branded a tritheistic or modalistic heretic. Despite all this, belief in the Trinity remains the touchstone for mainstream Christian orthodoxy, even though the people wielding the touchstone have no idea what it is or what it consists of. The Trinity is just a superstitious word that adherents of mainstream Christianity have to pay lip service to, lest they be thrown out of the synagogues by those who think they are serving God (John 16:2).
As mentioned above, Trinitarian apologist James White has repeatedly said that 60 to 80% of confessing Trinitarians actually hold modalistic beliefs (here, here, here, and here). In other words, despite their nominal belief in the Trinity, they instinctively understand and read their Bibles with the comprehension that God is unipersonal and reveals Himself modalistically. The truth is that there is no text in the whole Bible that teaches that God is a Trinity consisting of three co-equal co-eternal god persons. As mentioned above, the Old Testament doesn't develop any system of Binitarianism, despite the repeated references to God and His Spirit. Some Trinitarians try to appeal to 1 John 5:7 as a proof text for the Trinity, but it says nothing about co-eternality and could just as easily be interpreted to teach Modalism. In fact, textual critic Edward Hills has argued that 1 John 5:7 is authentic but was illicitly removed from early manuscripts because it was perceived to teach Modalism, namely, that "the Father, the Son and the Holy Spirit were identical" (see p. 212 here).
The Bible teaches that God exists as one person (see Deuteronomy 6:4 NASB or JPS). To understand why it is important to correctly understand the nature of God, I recommend reading my article Modalistic Monarchianism, Trinitarianism, and the Atonement. To understand how to distinguish the Father and Son without falling into the error of seeing distinct god persons, I recommend the following article by Jason Dulle: The Acknowledgement and Proper Placement of the Distinction Between Father and Son.