Catullus 7

Catullus and Lesbia seem to be hitting it off.
Lesbia, clearly flirting with Catullus, asks him how many kisses she needs to give him.
Catullus, being the hopeless romantic he is, writes a freaking POEM as an answer. And a lofty, grand one at that.

He uses imagery in this poem like an AP English student uses Sparknotes. He compares the number of kisses to such epic things as the grains of the Libyan sand "that lies on the silphium-bearing Cyrene" or are the stars. The poem is exceedingly pretty, giving personification to the night sky and invoking references to the Roman gods.

Catullus outright tells her how crazy he is about her. By comparing kisses to grains of sand and stars, he tells her that he will never have "more than enough" of her, and will truly love her forever. Finally, he staunchly declares that no one will find out about their affair or curse it. Apparentely Catullus is aware of the risks that having such an affair entails. But this time, instead of asking the gods for help, he promises to protect their love himself. Looks like love has created a hero out of him.

Catullus 43

In this poem, Catullus describes a girl who many believe to be beautiful, even comparing her to Lesbia. It is a poem that delivers a bitter attack against what Catullus believes is a "tasteless and crude age." It is also a poem that defends his beloved Lesbia.

He saultes the girl and talks to her directly, showing that he probably knew her in person. Catullus employs the device of litotes heavily in this poem. He takes many of the girl's features, and denies their beauty by stating their opposite. She has a nose that is not small, a foot that is not beautiful, and eyes that are not black. By declaring her features to be the opposite of beauty, Catullus reinforces the fact that he finds the girl ugly.

Perhaps the poem is a criticism of the decoctoris amica Formiani, who is clearly disliked by Catullus. And because she is the friend of said man from Formiae, he also must be a jerk face who needs to be put in his rightful place by Catullus.
Finally, the poem could just be a defense of Lesbia. Catullus is so in love with her that he can't have anyone believing that there might be someone beautiful than her. That's some strong devotion.

Catullus 109

At this point in their story, Catullus and Lesbia have met, spoken, and are together. Whatever that may mean.

In lines 1-2, Catullus says that Lesbia has made vows of everlasting love to him. However, he prays to the gods that she is able to keep this promise vere, sincere, and ex animo. He asks them to extend their promise of friendship for all of his life.

Catullus here tells us that Lesbia is fickle. Why would he need to pray to the gods if she was a truthful and sincere person who spoke her promises from her heart? What is more, he does not ask the gods to remove any obstacles from their love, even though Lesbia is married. If her husband was a problem, he would have asked the gods to take him out of the picture. However, he does not do that. Catullus seems to have great confidence that Lesbia will do whatever her heart desires - trivial things like obstacles are clearly not a problem for her. Lesbia has power and control. Catullus further prays that their contract of sacred friendship will last. Why does not he use the word love, as he did in the first couplet? Perhaps he hopes that even if his love does not, his friendship with Lesbia will. The last thing Catullus wants is for Lesbia to ignore or forget about him, because, as he knows, that is the true opposite to love.

Catullus 83

Finally we have proof that Lesbia knows of Catullu's existence! Hurray for Catullus!
Apparentely, all Lesbia does is bad-mouth Catullus in front of her husband. Catullus, once again seized by jealousy, acts superior while calling the husband "fatuo" and "mule", and then asking him if he really does not understand anything. Catullus claims that if Lesbia were to ignore him, then it would prove that she was normal and therefore did not have any feelings. However, Lesbia does not ignore or forget Catullus - in fact, she can't seem to get him our of her mind.

This is great news for Catullus, because, according to him, the more Lesbia talks about him, them more she will be drawn to him. He makes it a point to say that she burns, uriter. Catullus seems greatly hopeful that Lesbia will come to have even stronger feelings for him. Of course, love and hate aren't all that different in their intensity. He seems completely confident that this burning, passionate annoyance that Lesbia has for him can and will easily change into a burning, passionate love.
According to Catullus then, it is completely okay if someone dislikes you - as long as they can't move their thoughts from you, you win.

Catullus 2

Catullus once again dwells on the small details of his lady to satisfy his infatuation with her. In Catullus 51, he was jealous of the man who sat beside her; now he is jealous of her sparrow. He dwells extensively on the relationship the lady (most likely Lesbia) has with her sparrow.
This is yet another way that Catullus describes the qualities of his lady. She is quaint and charming, a girl who men are attracted to because of her lovable demeanor. He also hints that she is only playing with her sparrow to take her mind off of her own past lover. Whatever has happened between them, Lesbia is now looking for "some small relief from her pain." Catullus claims that she makes the sparrow peck her so as to forget her deeper, more agonizing pain - that of love.
However, Catullus is once again a cowardly figure in this poem. He does not approach Lesbia; he just watches her from afar. For whatever reason, Catullus cannot approach Lesbia. Even though he asserts that he would give the world to play with her as she plays with the sparrow, he cannot find the courage to even speak to her. He wants her to "ligthen the gloomy cares of [his] heart," yet he is most likely observing this scene from behind a far-off wall.

Creeper.

Catullus 51

Catullus 51 is a "translation" of a Greek poem written by Sappho. Sappho's original however, slightly differs from Catullu's adaptation.

Sappho's poem is highly personal, betraying her deep feelings for her lover. She is so infatuated that she even compares the man sitting next to her lover as a god. She describes in detail the qualities of her lover, from the "sweet murmur" of his voice to the "enticing laughter." Sappho asserts that she is so overcome by her deep feelings that she is even close to death.
Catullus seemed to admire Sappho, for he uses his poem as a sort of tribute or at least acknowledgement to her. Indeed, the opening line of his poem is a direct reference to Sappho's. Catullus also feels a deep, intense longing for Lesbia. He speaks of this longing as something that he cannot control, something that causes him so much pain that it "rips all his senses from him." Catullus and Sappho are both speaking of a feeling that everyone has felt at least once, a rush of love for someone who you might have just watched from afar.
However, Catullus differs from Sappho in his last stanza. While she fades away in the intensity of her love, Catullus stops abruptly and almost chides himself. He scolds himself for being in a state that has "previously destroyed kings and happy cities." Perhaps he has been rejected, and is angry at himself for spending so much time on a love that won't pay him much heed. Or even if his affair has gone well, he feels that he is just wasting his time - yet another feeling that people who have had experience with relationships can relate to.