The Shri Stuti composed by Shri Vedanta Deshika consists of 25 shlokas. A summary is available here. The exploration here is to get at the meanings of each of the
words, investigate roots and related words.

[1] "The Practical Sanskrit-English Dictionary" by Vaman Shivram Apte, Revised and Enlarged Edition, Motilal Banarsidass Pub
[2] "Shri Desika Stotra Mala" by Shri Ramadesikachariar Swamy, 2003 Edition, Lifco
[3] "A Sanskrit English Dictionary", M. Monier-Williams, Motilal Banarsidass Publishers

[Invocatory Tanian on Swami Desikan by Kumara Varadacharya]

    shrImAn ve~nkaTanAthAryaH   kavi-tArkika-kesarI
    vedAntAcArya-varyo me       saMnidhattAm sadA hR^idi

    
    
[01.txt]

    mAnAtIta-prathita-vibhavAM ma~NgalaM ma~NgalAnAM
        vakShaHpIThIM madhu-vijayino bhUShayantIM svakAntyA
    pratyakShAnushravika-mahima-prArthinInAM prajAnAM
        shreyomUrtiM shriyam asharaNastvAM sharaNyAM prapadye

    

[02.txt]

    AvirbhAvaH kalasha-jaladhAvadhvare vA$pi yasyAH
        sthAnaM yasyAH sarasija-vanaM viShNu-vakShaHsthalaM vA
    bhUmA yasyA bhuvanam akhilaM devi divyaM padaM vA
        stoka-praj~nairanavadhi-guNA stUyase sA kathaM tvam

    


[03.txt]

    stotavyatvaM dishati bhavatI dehibhiH stUyamAnA
        tAmeva tvAm anitaragatiH stotum AshaMsamAnaH
    siddhArambhaH sakala-bhuvana-shlAghanIyo bhaveyaM
        sevApekShA tava caraNayoH shreyase kasya na syAt

    

[04.txt]

    yatsa~NkalpAdbhavati kamale yatra dehinyamIShAM
        janmasthema-praLaya-racanA ja~NgamAja~NgamAnAm
    tat kalyANaM kimapi yaminAm ekalakShyaM samAdhau
        pUrNaM tejaH sphurati bhavatI pAdalAkShArasA~Nkam

    

[05.txt]

   niShpratyUha-praNaya-ghaTitaM devi nityAnapAyaM
       viShNustvaM cetyanavadhiguNaM dvandvam anyonyalakShyam
   sheShashcittaM vimala-manasAM mauLayashca shrutInAM
       saMpadyante viharaNavidhau yasya shayyAvisheShAH

    
          
[06.txt]

    uddeshyatvaM janani bhajatorujjhitopAdhigandhaM
        pratyagrUpe haviShi yuvayorekasheShitvayogAt
    padme patyustava ca nigamairnityamanviShyamANo
        nAvacchedaM bhajati mahimA nartayan mAnasaM naH

    

[07.txt]

    pashyantIShu shrutiShu paritaH sUri-bR^indena sArdhaM
        madhyekR^itya triguNa-phalakaM nirmita-sthAna-bhedam
    vishvAdhIsha-praNayini sadA vibhrama-dyUta-vR^ittau
        brahmeshAdyA dadhati yuvayorakShashArapracAram

    
      
[08.txt]

    asyeshAnA tvamasi jagataH saMshrayantI mukundaM
        lakShmIH padmA jaladhi-tanayA viShNu-patnIndireti
    yannAmAni shrutiparipaNAnyevamAvartayanto
        nAvartante durita-pavana-prerite janma-cakre

    

[09.txt]

    tvAmevAhuH katicidapare tvatpriyaM lokanAthaM 
        kiM tairantaH kalaha-malinaiH kiMciduttIrya magnaiH 
    tvatsaMprItyai viharati harau saMmukhInAM shrutInAM
        bhAvArUDhau bhagavati yuvAM dampatI daivataM naH

    
      
[10.txt]

    ApannArti-prashamana-vidhau baddha-dIkShasya viShNoH
        AcakhyustvAM priya-sahacarIm aikamatyopapannAM
    prAdurbhAvairapi sama-tanuH prAdhvam anvIyase tvaM
        dUrotkShiptairiva madhuratA dugdharAshestara~NgaiH

    

[11.txt]

    dhatte shobhAM hari-marakate tAvakI mUrtirAdyA 
        tanvI tu~Nga-stana-bhara-natA tapta-jAmbUnadAbhA
    yasyAM gacchantyudayavilayairnityam Ananda-sindhau
        icchA-vegollasita-laharI-vibhramaM vyaktayaste 

    

[12.txt]

    AsaMsAraM vitatam akhilam vA~NgmayaM yadvibhUtiH 
        yadbhrUbha~NgAt kusuma-dhanuShaH ki~Nkaro meru-dhanvA
    yasyAM nityaM nayana-shatakaireka-lakShyo mahendraH
        padme tAsAM pariNatirasau bhAva-leshaistvadIyaiH

    

[13.txt]

    agre bhartuH sarasija-maye bhadra-pIThe niShaNNAm
        ambho rAsheradhigata-sudhA saMplavAdutthitAM tvAm
    puShpAsAra-sthagita-bhuvanaiH puShkalAvartakAdyaiH
        kL^iptArambhAH kanaka-kalashairabhyaShi~ncan gajendrAH

      

[14.txt]

    Alokya tvAmamR^ita-sahaje viShNu-vakShaHsthalasthAM
        shApAkrAntAH sharaNam agaman sAvarodhAH surendrAH
    labdhvA bhUyastribhuvanamidaM lakShitaM tvatkaTAkShaiH
        sarvAkAra-sthira-samudayAM saMpadaM nirvishanti

     

[15.txt]

    Arta-trANa-vratibhiramR^itAsAra-nIlAmbuvAhaiH
        ambhojAnAm uShasi miShatAm antara~NgairapA~NgaiH
    yasyAM yasyAM dishi viharate devi dR^iShTistvadIyA
        tasyAM tasyAm ahamahamikAM tanvate saMpadoghAH

      
  
[16.txt]

    yogArambha-tvarita-manaso yuShmadaikAntya-yuktaM
        dharmaM prAptuM prathamam iha ye dhArayante dhanAyAm
    teShAM bhUmerdhanapati-gR^ihAdambarAdambudhervA
        dhArA niryAntyadhikam adhikaM vA~ncchitAnAM vasUnAm
         
       

[17.txt]

    shreyaskAmAH kamala-nilaye citram AmnAya-vAcAM
        cUDApIDaM tava pada-yugaM cetasA dhArayantaH
    chatracchAyA-subhaga-shirasashcAmara-smera-pArshvAH
        shlAghAshabda-shravaNa-muditAH sragviNaH sa~ncaranti
 
        

[18.txt] 

    UrIkartuM kushalam akhilaM jetum AdIn arAtIn
        dUrIkartuM durita-nivahaM tyaktum AdyAm avidyAm
    amba stambAvadhika-janana-grAma-sImAnta-rekhAm
        Alambante vimala-manaso viShNu-kAnte dayAM te
         
    

[19.txt]

    jAtAkA~NkShA janani yuvayoreka-sevAdhikAre
        mAyAlIDhaM vibhavam akhilaM manyamAnAstR^iNAya
    prItyai viShNostava ca kR^itinaH prItimanto bhajante
        velA-bha~Nga-prashamana-phalaM vaidikaM dharma-setum
        
    

[20.txt]

    seve devi tridasha-mahiLA-mauLimAlArcitaM te
        siddhi-kShetraM shamita-vipadAM saMpadAM pAda-padmam
    yasminnIShannamita-shiraso yApayitvA sharIraM
        vartiShyante vitamasi pade vAsudevasya dhanyAH
        
    

[21.txt]

    sAnuprAsa-prakaTita-dayaiH sAndra-vAtsalya-digdhaiH
        amba snigdhairamR^ita-laharI-labdha-sabrahmacaryaiH
    dharme tApa-traya-viracite gADha-taptaM kShaNaM mAm
        Aki~ncanya-glapitam anaghairArdrayethAH kaTAkShaiH
        
    

[22.txt]

    saMpadyante bhava-bhaya-tamI-bhAna-vastvatprasAdAt
        bhAvAH sarve bhagavati harau bhaktim udvelayantaH
    yAce kiM tvAm aham iha yataH shItalodAra-shIlA
        bhUyo bhUyo dishasi mahatAM ma~ggaLAnAM prabandhAn
        
    

[23.txt] 

    mAtA devi tvamasi bhagavAn vAsudevaH pitA me
        jAtaH so$yaM janani yuvayorekalakShyaM dayAyAH
    datto yuShmatparijanatayA deshikairapyatastvaM
        kiM te bhUyaH priyam iti kila smera-vaktrA vibhAsi
        
    

[24.txt]

    kalyANAnAm avikala-nidhiH kA$pi kAruNya-sImA
        nityAmodA nigama-vacasAM mauLi-mandAra-mAlA
    saMpad-divyA madhu-vijayinaH sannidhattAM sadA me
        saiShA devI sakala-bhuvana-prArthanA-kAmadhenuH
                
    

[25.txt] 

    upacita-guru-bhakterutthitaM ve~NkaTeshAt
        kali-kaluSha-nivR^ittyai kalpamAnaM prajAnAm
    sarasija-nilayAyAH stotram etat paThantaH 
        sakala-kushala-sImAH sArvabhaumA bhavanti 
         
    

[Valedictory Tanian on Swami Desikan by Kumara Varadacharya]

    kavi-tArkika-simhAya        kalyANa-guNa-shAline
    shrImate ve~nkaTeshAya      vedAnta-gurave namaH