積みます
 

Hi, I would like to know if both these sentences are correct?

材木をトラックに積む
Load lumber onto the truck

トラックに材木を積む
Load lumber onto the truck

テーブルに本を積みます
Pile the book up onto the table

All correct.

Regarding the last sentence, though, a native speaker would picture more than a few books getting piled up.

Thanks for the help, masaegu san. :)

I have another question which is regarding translating "I will not give up" into Japanese. Should I say "僕はあきらめない" or "僕があきらめない"?

I am still having many problems with particles such as "が", etc. Anyway, there was this song title "僕が僕であるために" and I am very curious to know what does it mean?

You should definitely use 「僕はあきらめない」.

Say it with が and we won't even know what you're talking about. We would ask you "Who is/are the other guy/guys that you're talking about?" I am not exaggerating one bit here. If you place extra stress on the word "I" in the sentence "I won't give up.", that's the equivalent of 僕があきらめない.

Use はwhen you simply want to say "I do/don't ~~~.", "I am/am not ~~~.", etc.

Use が when saying "I am the one who ~~~." It's not Tom and it's not Mary but it's you.　It's you out of a group or out of the whole world.

「私が買った車」= the car that I bought. It's not anyone else's car but yours. Native speakers, including toddlers, will NEVER say this with は.

Maxful: 誰がコンビニに行ってきてくれる？ Who will go to the convenience store for me?
Masaegu: ボクが行きます。　 I will.
This is が　100% of the time. You are volunteering to go out of the group.

When you can use all the particles correctly, that's when your Japanese studies end. So, it will never end.
_________

僕が僕であるために = For me to be me. In other words, "For me to be myself"

Masaeguさん、本当にどうもありがとうございました。I will give it a try now and please check if I am correct.

Face to face:

先生：あなたはどなたですか。

田中：私は田中ですよ。


In the class/office with a group of people:

先生：田中はどなたですか。

田中：私が田中です。

That is precisely how you use it!

(Since どなた is nice and polite, it would sound better if you added さん to 田中 in the second example.)
__________

If I may ask a question using your good examples, in which situation can Tanaka simply say 田中です without the pronoun + particle? This may look like a dull question but it should actually teach you something about は/が from a different perspective.

I am not sure, to be honest. 説明してもよろしでしょうか。:)

Masaeguさん. Then is it correct saying that if I reply 僕は行きます you will assume that I might go to the shop alone, but I might as well go with someone else?
Someone once told me that は assumes a value of "at least". Yet, is that why you prefer using は with negative phrases? I know they might sound silly questions, but Maxful is right...は and が is a topic that Japanese learners will never understand 100% :)

P.S. 田中です goes with the が phrase? Since it is an absolute remark that leaves no doubt it should go with an absolute certainty and 僕が offers it.

Sorry, I doubt "説明してもよろしでしょうか" is correct.

”説明ができますか”

OK but that means "May I explain?" :)

You can say:
説明していただけますか。
説明してください。
説明をお願いします。
etc.
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿

1. Face to face:
先生：あなたはどなたですか。
田中：私は田中です。

2. In the class/office with a group of people:
先生：田中さんはどなたですか。
田中：私が田中です。

The answer is #1. As you already know, we don't use pronouns too often. You can say 「田中です。」、「田中といいます。」、「田中と申し ます」 to mean "My name is Tanaka." We rarely use first-person pronouns to tell names because the listener(s) will know for sure whose name it is that you are telling them. In this situation, the pronoun is not important in the Japanese culture (& language). We can perfectly communicate without using one.

In #2, however, you cannot just say 「田中です。」. Why not? Because your teacher already has the name 田中. S/He just doesn't know which one of you is 田中.　Accordingly, you cannot omit the first-person pronoun. 「私が田中です。
」 means "I am Tanaka." with the accent on the "I". The pronoun here is very important unlike in #1.

The reason I asked this question is to illustrate the fact that there is always a reason for using が. When you use は, "the subject + は" part may often be omitted but it will not hurt the communication.

Not so with が. "The subject + が" cannot be omitted for comunication. I wish I could show you how to say the answer part of each example. The 私 part in 私は and 私が must be pronounced with a striking difference. Same thing with "I do." and "I do."